I'm going to separate verisimilitude (a believability within a fictional setting), constancy (the physical and other 'rules of the world' are interpreted consistently within the game rules and the GM's sessions), and realism (some sort of notion of what things would be in the real world outside of the game universe).
Realism, by itself, is neither good nor bad. But it can be contentious. But also a lack of some common things behaving as they would in the real world can be a problem.
There used to be some sort of convention in sci-fi (vs. space opera) that you got to have one or two McGuffins (things which we think now are not possible or that could be possible but we have no idea how or which break things we think are universal physical limits) in any novel. Then you usually make these items either key parts of the background setting for your story or you make it a critical part of the story itself.
I sort of figure on something similar needs to exist for 'low fantasy/iron heroes/settings you want to feel more akin to our medieval period'. For 'high fantasy' (analogous to space opera), many more areas behave different than we would expect in the real world.
Constancy, on the other hand, in adjudication and within the rules themselves, is a critical part of the ability of players and the GM to have a world that does not seem arbitrary or without any common understandings. Where constancy is broken, rulings will tend to contradict one another and players and the GM can really get into arguments and misunderstandings.
So Realism as such isn't critical, but Constancy is, even in high fantasy and wild genres.
These two together lead to this statement: Whatever your setting is, whatever few or many divergences from physical reality (be it physical laws, character abilities, magic, economics, etc), once you set them down and agree on them as a group (GM and players), the interpretations should be constant within that particular environment.
Verisimilitude is a bit different but also important: Whatever changes to real world reality that the rules or the setting of the GM or the GM's presentation of sessions, each of those needs an in-game logic and that logic should be understandable and seem reasonable given the nature of the setting. Internal consistency is another way to look at it within the context of your particular fictional environment.
Examples that I have run into that bothered me over the years:
3.5E -> It took me until the high teens and a specific build to be able to have my very strong character with many levels of warrior training to be able to shove back an enemy in melee (by physical strength or a shield rush). I think I was at least level 14 or 15. So it was impossilbe for a lower level character to break a battle line even if they were bigger, stronger, and more trained and experienced than their foe until you got to higher levels because the game designers wanted to have some things give to players in the late levels in the way of special effects. In AD&D, where these things were handled badly (mechanically) also, you could at least attempt to knock someone down or back because there was a method anyone could use or because it wasn't covered and the GM would probably come up with a probability and you'd roll.
4E -> Dissociated mechanics like the cleric attacking and it healing everyone around him/her. What? Why? (Why was 'we want the cleric to do more with his encounter than heal,heal,heal,heal,heal!) The meta-game concern was a valid one for Clerics, but the mechanic provided was not really much good for in-universe logic.
Any version without arcane spell feats: I can produce a massive blast of fire, but it can only be shaped as a sphere (or square for the 4E crowd which is bizarre given it was a 'ball' of fire). Really? What would it have hurt to let the player have more shaping? And why is it useful to have every mage have to engage with a whole feat tree to get some useful options when it comes to how they manipulate their magic?
The 20x20 room with the ancient red dragon and a standard door. How did the dragon breathe in there? Where did any droppings go? What did it eat? Where did it get water from? etc. (terrible things done by just plopping creatures into potpourri dungeons with no sensible explanation within the fiction of the game)
So those are just some of the things to me that didn't make sense.
I can also show that realistically, most people didn't carry 4 lb longswords. 1.5 to 2 lbs for people that have to use the sword a lot because 4 lbs is too heavy to hold and swing vigorously for long periods in a fight. Coins were often 100s to the pound of weight, not the 20 per pound or whatever it was in earlier games where you must have been trading gold and silver frisbees instead of what the real world had. Rope is also hilarious: I did some research on hemp rope and on working loads with significant safety factors to handle the 'drop and suddenly get decelerated by the rope' scenarios. The weights for lengths in D&D come closer to (IIRC without looking at my revised table) would mean you were carrying a 2" rope. Most parties would be able to manage with a 3/8" rope and 100' of it would still be less weighty than the standard D&D rope. And for carrying stuff, how you carry it matters. Backpack over in your hands means you can actually carry more. Framed pack with the appropriate strapping also means that you can carry even more with more comfort for a longer period of time. And clothes at 4 lbs? Depends on the clothes and the climate. And some of the slow downs for armour were ridiculous and not in line with historical realities as of at least 25-30 years ago.
But do those things matter? Yes and no.
First, it depends on your player group. One player group I've got includes two history majors with focus on medieval or roman times, another group has serving military folks well versed in US Civil War and Ancients, another in Age of Sail. Several player groups include campers and mlitary people who have a good idea what you can and can't carry and for how long from practical experience. And we've all found too much magic not sufficiently thought out in the setting and rules or rules that were setup for meta-game things vs. to feel right in the setting tended to cause troubles in expectation by the player and the GM (when what you think you expect is not repllicated in the game, much like the high level I needed to attain to knockback enemy line of battle combatants).
I as a GM wanted to have a somewhat reasonable idea of how many folk could live in an area, how areas would grow, how greater fecundity would affect population growth, etc. and so I talked to a friend who is one of the world's best animal population modellers to get a simplified but useful set of equations to simulate growth in my fantasy world.
Why does a coin being 200 to a pound vs. 10 or 20 per pound matter? Because when you take a moment to think about it, what was the point of coins? Commerce. It is sometihng that has value and I can move that value around, pay for things, and earn for labours. If I have 10 per pound, you have to pay 1/10th of a pound for anything. If you have 200/pound, then you can pay for things with 0.5% of a pound. Similarly you can earn money in more useful amounts. And it makes carrying arouund basic necessities much lighter and yet still useful. There's reasons they broke them up into small sizes - fits in purse, doesn't tear the bottom out of purse, can make useful tokens of value in economies that were silver standard and there's no way anyone but the King might buy a 10 gp meal.. (a pound of gold, given how hard it is to find, dig out, purify and then turn into coins? GAH!).
So if you never think of these aspects of your world, 10/pound is fine. If you think about the setting much and think 'Wouldn't it make more sense to have smaller units that are easier to carry given how hard it is to get out of the ground?" then you start to wonder about the game designers thinking.
And that's why there are some good reasons to borrow (for small mundane things like currency weights, costs of food/lodging, annual incomes, weights of historical weapons and tools (rope!), and so on) from the real world - then you don't have people thinking about the setting and saying 'Why would they do that?' and force you to come up with some weak and unlikely explanation when it was simply poorly construed in the rules handed to you.
And my groups are almost all college or university types (many with real world military or travel experience, some that are even archaologists) and they think about settings and details and things that seem odd.
Other groups I've played with were very okay with whatever the game said because they never looked very different.
When you have mundane physical things in a fantasy world, and you don't say 'all weapons are built extra sturdy because metalurgy is terrible here' or 'ropes here are less strong than real world ropes because of poorer plant material' then (devoid of that explanation) people will fall back for the mundane onto physical things they know from the world. And if the rules or the GM's setting violate those simple and well known behaviours, it strains verisimilitude and causes misunderstandings and often arguments.
So to recap:
Constancy is ruling and in internal logic within the fiction is the most important aspect of setting and gameplay you can provide as a GM.
Verisimilitude means you just have to explain things that depart from the norm in the real world we know and come equiped to recognize sufficiently such that your players feel there is an in-fiction explanation that passes at least modest scrutiny.
Realism is only useful in that it aids in Versimilitude for all the things we don't want to explain as being strange or very different than the real world. When you don't want to have to explain why something differs from reality, then steal from reality.
That's if you have folks that like to look at the larger setting and immerse themselves in it and understand it as they do in the real world.
If people in your group treat the settings as a facade they throw up at a theater for a 15 minute scene, then you probably don't have to worry overmuch what it looks like or how it works because they aren't likely to care - their forcus is on the actions they will get to do on the stage in the scene.
Neither view of the world is better or worse, but you better know who you have in your play group and how they think and how deeply they think about the world you are presenting and the rules that let you operate in them.
In my group, when in doubt, I look to real world to help as to 'How many knights and manors are there in the County?' or 'How many soldiers can I levy with a grain tax?' etc.
Good topic, but it totally depends on your player group and there interest in immersion in the setting as a living breathing system vs. as a painted background for cool party actions.
Mine want both
