The rules can be different, as long as they exist and are knowable. Otherwise, it's just the DM making stuff up and expecting the players to go along with it, when they have no way of knowing what makes sense or not.
Whether an ogre can knock over a tree, or not, can't just be a matter of genre convention. Different people have different expectations about how the the world should work, and the rules in the book exist so that we can all be on the same page about what exactly makes sense for the world. Without some sort of rules to cover this situation, the player can't play their character, because they have no idea what sort of world they're living in.
I don't know if I agree that this example would be so disruptive to immersion within the fictional world. I understand your point, but I don't think that having the ogre function differently in some ways than PCs is all that big a deal. I mean, certainly there are creatures in the world that can do things the PCs cannot do. There is presumably some creature out there that can knock the tree down...a dragon or a storm giant or a titan, what have you...and it sounds like most folks would accept it in those cases.
So the issue seems to stem from the fact that the players KNOW that the ogre has a 19 STR and that so do they (or so one or two of them may have). So if that is the issue...the perceived parity of STR between the PC and the ogre...then for me the answer is to eliminate that expected parity.
I don't think this is removing the rules of the fictional world so much as it is redefining them. Such a redefinition may or may not be suitable or accepted by the group....so I certainly am not saying this is an approach for everyone. I just don't think that we need to adhere to such clearly defined mechanics at all times.
This is an interesting take.
As far as the ogre/PC reciprocity is concerned, PCs can become large via spells, potions etc so I'm not sure that solves all the issues.
I'd treat a PC who grew to large size through magic in much the same way, I think. Just let the tree be knocked over...let the chance of failure or success in the scenario stem from whether the tree hits the intended target. No need to double the amount of checks required.
But the idea that an ogre's STR stat is there only to manage combat stats is interesting. It's almost the inverse of AD&D, where an ogre's 18/00 STR didn't inform it's combat stats at all (attack as a 4+ HD monster, for 1d10 or weapon+2) but did inform it's out-of-combat abilities. One reason AD&D could go for ogre/PC parity in this respect was because it used non-linear bonuses (eg via Bend Bars or "open wizard locked doors" chances) and because very few PCs could get to 18/00 STR without becoming enchanted beings by using wishes, magic books and/or gauntlest/girdles. In other words, letting an AD&D character roll the chance to force a wizard locked door as the chance to knock down a big tree won't create any issues, because only those with STR 18/91 or better have any chance at all, ogres only have a 2 in 6 chance, and there are no retries.
Bounded accuracy + linear bonus progression changes all this. And so creates this pressure to divorce the ogre's capabilities from its ability scores. Which is what 4e did, by locating a lot of this stuff in "powers", and by using "genre logic" rather than "objective DCs" as the gateway to improved stuff.
Yeah, I think with 5E, the math seems mostly based on combat and with bounded accuracy in mind. I really don't think that the designers intended for an ogre to be limited to human level feats of STR. I mean, looking at the appearance of the ogre as depicted in the Monster Manual certainly doesn't give me the impression of a creature whose strength is equal to that of a very strong man.
I see a distinction in a STR score for creatures of varying size. I do t think that's a problem overall, nor that it must lead to inconsistency. I think that it's just a matter of putting some of this on the DM rather than in another area, like the powers of 4E as you mention.
A player can be discouraged after seeing a cool move used if they are told "Not for you! It doesn't matter that you are stronger than an ogre and the same size, I don't think you should be allowed to shine like this".
I can see the problem with that in general, sure. I don't know if I think it applies in this instance since PCs are not the same size as ogres. Not without some kind of magic...in which case let the PC succeed because hey, magic!
But I think this view also implies there should be nothing that the PCs see an NPC or monster do that they cannot, no? So I don't know if this is a real strong way of looking at the issue. Some creatures can and should be able to do things that the PCs cannot. And vice versa, of course.
For many people, an ogre pushing down a tree in a single round (since multi-hundred horsepower tractors can't pull the things down in less than 5 minutes AND it takes more than 6 seconds for a cut tree to fall) IS displaying a strength the ogre shouldn't have. So the players at the table: are they going "Cool!" or are they going "Hmm, what's going on? Is it just the DM playing around or is something we should have caught? Quick! Are there other clues we overlooked?"
This is true, but again I think this all relies on a good deal of meta knowledge and then using that in play. Obviously, for games that have already established how all this works, it would be harder to adjust. But for players who don't know that the ogre has a 19 STR, or those who aren't as concerned about the mechcanical implications of that 19, it's likely not an adjustment at all.
Sure I trust my GMs making judgements inside the games we agree to play; that's their role. Because I trust them to operate within those parameters that using the rule of cool in a game designed without it is so jarring for me as a player. I'm the guy constantly looking for discrepancies -- not to hoist the DM on his petard, but to use to discover hidden features that are either neat or advantageous in the game world.
I don't know if the rule of cool is something barred from the game. It's not specifically referenced on the books, but there are plenty of areas where it or something like it seems to be implied. Plenty of times where DM judgment is not just recommended, but absolutely required.