Because due to both physical limitations and (sometimes) local laws we have to abstract nearly all the physical activities our characters do. We can't climb walls at the table, nor balance on clifftops, nor throw heavy objects, nor - most importantly - fight each other. LARPing gets around some of this, but by no means all of it; and with the rarest of exceptions D&D isn't a LARPG.
This is a reason to treat
all stats this way, not to treat only some. We cannot translate fictional languages. We cannot cast spells. Etc.
Therefore, the stats relevant to those physical activities are going to meet game mechanics on a frequent and recurring basis in order to carry out these abstractions. And as such, those stats are very much going to inform play.
Players can, however, think and talk* at the table pretty much directly as their characters would in the fiction, with far less abstraction required. Here, though, in order for the non-physical stats to inform play on a vaguely equal basis with their physical counterparts, it's on the player to not only let that stats-inform-play process occur but to lean into it fairly hard.
Otherwise the players might as well just play their real-life personalities in the fiction, which will get pretty boring over the long term.
* - with all the in-fiction languages conveniently translated to English or whatever other language is spoken at the table, of course.
Again this is completely spurious. What differs in this from--say--a player who has stage fright being incapable of giving a rousing speech? A player who has discalculia being incapable of doing complex arithmetic? A blind player failing to visually poke at every nook and cranny?
Players can move and bend and jump and endure. Why do those get dismissed as "well it would be too difficult"? Who the heck cares? You've just responded with circular logic. If you already aren't asking the player to
physically look at details in order to perceive them within the game, you're already accepting that mental scores have uses which aren't tied to actions of the player. Likewise, if you had an actual gymnast in your group, and said gymnast showed you that it was physically possible to do something you thought couldn't be done, would you continue to reject their character's ability to do it? Or would you grant it, since you'd been shown IRL that it was in fact doable?
Given I consider you a relatively reasonable person, I would think you'd accept a physical demonstration like this. But that would mean you'd account for physical things your players can do, as part of what stats can do. Likewise, I doubt you demand players physically search every corner of a physical room in order to find objects--the player has to show
initiative, but the actual observing is trusted to mechanics, no? At which point we have counter-examples in both directions: a player using their physical ability to demonstrate that something can be done, and a player
not using their own IRL capabilities but instead relying on mechanics.
Yes, I grant that many physical feats are things a player cannot personally do. The exact same logic applies to mental feats. There are some people can do, and some they can't. To demand perfect represntation of the mental and zero representation of the physical remains unjustified--because exceptions are allowed in both directions.