Just wanted to hone in on this part.
It's not a matter of finding support for this position in the text (which, as you imply, does not exist), it's also about balance and intrusions on design space. For instance, if anyone can disarm an opponent, the battlemaster's disarm maneuver feels less special. It certainly seems like disarming an opponent should be an option for any combatant, but allowing it devalues the fighter.
I really, really don't think it does. The only way you get to this point is if the player assumes an
exclusive right to certain actions. Without that assumption, there is nothing to "devalue." And with it, you have assumed a very severe and likely impossible standard, which literally does say "no one can EVER improvise something like my character! That's STEALING my character!"
Where does this "I *exclusively* own the mechanics of my character" thing come from? It's both fundamentally silly, and overtly contradictory to the goals expressed by the game and literally every DM I've ever actually spoken to. So from whence does it come? And why is it that, despite the mortal fear of it (which seems to drive many good DMs to excessive, even draconian limitations on their players), I've *never* seen it actually happen in play, even in games where it is allegedly a deeply-rooted flaw e.g. 3e/4e?
Balance considerations don't even enter into it. The feat (as noted) *guarantees* access, which is soft-balanced against the combined issues of justification and rolling--again, the "DM needs a reason to say no to a feat, or yes without one." That doesn't mean it needs to be hard in either case. Of course, DMs being human, it takes practice and caution to thread the needle between "discouraging improvisation" and "being permissive." I tend to lean toward the latter; I find most DMs lean the opposite way out of *fear* of permissivity, and then can't understand why people at their tables stop trying. But balance is totally achieveable in this.
In the same sense, if players can do feat-like actions without having the feat, you devalue the feat. At least, that's a perspective espoused by some people. I don't buy into it much. I allow people to do several feat-like actions, but there's usually a penalty involved that a person with the feat wouldn't suffer.
Right; lack of automatic access, and needing to work/justify ARE the penalty, or determine what it is. From them, things arise like "okay, you are familiar enough with her voice to try to imitate it, but she's a Dragonborn and you aren't. How do you overcome the differences in physiology?" If I don't like the answer? I may literally just say they know they can't pull it off well enough to pass muster unless they're desperate. (I hate hate hate the false hope of "I'll let you roll but you need 18+ to succeed.") If it's barely enough, a paper-thin plan but a plan nonetheless, roll with a penalty (or disad, though I
despise how 5e defaults to that). If it's a good plan, you work hard or spend resources? Sure, roll it. And, as noted, I've never once seen, neither as player nor in my brief experience as DM, even ONE player who got even a little upset at this kind of thing. (Besides, if the Actor isn't prevented from doing it herself, why is the non-Actor trying? The examples become more and more artificial the more I examine them.)
An aside (not to you specifically, Ezekiel), I expect creativity to emerge more through interesting character backgrounds and game play than game settings like feats/no-feats and filling out a character sheet.
This strikes me as another overblown fear (of players never thinking beyond numbers; it's a nicer/semi-polite way of saying, "I want roleplaying not rollplaying," IMO), but that's a topic all its own.