A similar conversation was recently had in the thread about using out of character knowledge. I believe that the view in opposition to yours (and to my preference) is that if the player wants to have their character think something - regardless of the mental stats - then they can. If they want their 3 INT character to think they know how to make gun powder, or all of the simple machines, or a printing press, or what the MM says about all of the monsters, or how integral and differential calculus, then that's fine. They might be wrong in that particular game world. While there were clear prohibitions of this in 1e and 2e, they do not exist in 5e. As such, it might be argued that requiring play that way is a house rule (and not just "common sense" as I might still say in spite of having found no 5e rules requiring it).
So how is it okay that that's the case with INT and WIS and CHA, but not with all stats? This is a clear double-standard, and one which isn't apparently well-supported by any kind of actual rationale beyond "I want it thatta way!", to quote the Backstreet Boys.
Players determine how their characters act, what they say, and how they think. A gorilla's Intelligence score has no bearing on how a character is portrayed unless the player decides that it does. You seem to say that you think it's somehow unfair that a player portrays an Int-5 character as something other than "thick." But again, you have nothing to back this up other than personal preference. A preference I don't share.
Actually I've demonstrated exactly why I think that, with an actual argument and rationale. You claiming it's nothing but personal preference isn't a counter-argument, it's just a lie, and a pretty cheap one. You can say you disagree with my rationale, or that my rationale is rubbish, but you can't lie and say I
didn't offer one. You've offered no rationale I can find beyond preference (maybe I just didn't recognise it?), and you're trying to suggest I'm doing the same, which is outright false.
For you it appears, reading between the lines, because you've not really explained your position that I can see here, is that mental stats are
meaningless except to rolls, and a PC is in no way bound or even to be influenced by them - correct me if I'm wrong here. Presumably in your game, I can dumpstat INT/DEX/CHA, then RP a brilliant, wise, incredibly charming character, and just be really surprised when the big penalties mean I fail at tasks involving those stats. Is that right?
Can I equally dumpstat STR/DEX/CON, and claim to be a musclebound athlete with top-notch endurance who has never been ill a day in his life? I doubt it, but if you say yes, at least that's consistent with stats being meaningless except to rolls.
I don't think anyone who worked on any edition of D&D intended it to be played that way, and seems like it's a case of "From my point of view, the Jedi are evil!" (I guess you're Anakin and I'm Obi-Wan in this scenario), but at least it would be consistent, and there are other RPGs which do abstract stats to that degree, making them more "narrative ability" than actual stat - i.e. INT would cease being any kind of measure of the character's actual intellectual ability, and merely instead become their narrative ability to succeed at tasks related to intelligence.
That's kind of fun on a certain level, but it's not viable if you don't do it with physical stats, and it's clearly not intended given the strong correlation between INT and described intelligence in the MMs, NPCs, and so on.
3 out of the 4 games I am involved in have rolled stats. I know 2 more ongoing games that also use rolled stats.
Your preference is subjective and arbitrary, and should not be presumed to be universal.
The above of course also applies to my preference, to everyone's preference, really.
Dude, let's stay in the real world here, instead of this fanciful realm where anything is possible, at least re: chargen. Every larger-scale survey of 5E players that I'm aware of suggests a minority of people roll their stats as their main method for playing 5E (specifically - OSR is a different story). Whilst I haven't seen many surveys about it, those who do roll, when it is discussed, seem to indicate they use pretty generous methods.
Your concern is only a real concern if you roll using a "down-the-line" method of rolling. I very much doubt that more than a fraction of a percentage point of 5E players roll "down-the-line", and even those that do probably don't use methods which can result in the stats you describe.
And if you are in a game that rolls "down-the-line", you know what you signed up for, which is to say, totally random stats which you then have to make the best of.