I disagree, for several reasons.
First, you don't have equal agency across all tables to "play act" what you want how you want. Look no further than the recent thread re playing characters not of one's own gender; or any thread regarding allowance of evil characters; or anywhere someone denigrates doing something "because it's what the character would do" even though following the character wherever it leads you is the purest form of RP.
These kind of arbitrary limitations IMO hammer player agency far harder than most of what's been discussed in here.
These are not restrictions
of the game. When discussing player agency, we're talking about how the game the player is playing enables or disables agency. These things you're talking about are social contract issues. I believe I just mentioned the problem of social contracts infiltrating understanding of how games work, and this is another excellent example.
Second, to blanket-declare that role-play isn't required by the game and-or isn't necessary to the game is in error; in that some systems (e.g. 1e D&D and some LARPs) actively reward "good roleplaying" (in 1e this is done via added XP, and faster/cheaper training at level-up).
Play-acting. Roleplaying doesn't require play-acting. And, play-acting is not necessary to any RPG. It definitely something I'd encourage anyone to do because it's fun and it adds to the experience, but the mechanics and systems of these games operate just fine without any play-acting.
Let's not do the confuse roleplaying with play-acting at that table. I'm roleplaying just by playing Bob the Fighter -- I've taken on the role of that character and will, to different degrees in different games, engage the game in the guise of that role. Me using a funny voice or 1st person doesn't really engage any mechanics of the games.
Caveat: It may engage the aspect of a game where the goal is to convince the GM, through entertaining them, to allow your character to do something. Come to think of it, this is a common thread for those arguing that play-acting is essential to RPGs.
Third, to say that role-playing isn't necessary in a role-playing game is...well, let's just say it's a bit much.
I agree, 100%, see above about the difference between roleplaying and play-acting. Or rather, that play-acting is just one way to roleplay.
That said, in the grand scheme of how various systems are written and intended this type of agency is probably more or less a wash, yes. But that it's a wash is no reason to discount RP-agency from consideration here; if for no other reason than not every table plays their system as written or intended and some tables/GMs in fact do deny RP agency on a regular basis.
There's no such thing as a game feature that enables or disables players from being able to play-act their characters. It's orthogonal to the issues discussed. Any agency involved in play-acting is outside the game, not inside it; ie, it's a function of what's acceptable at your table.