But it can't. I mean, it literally can't. What it should be is an entirely different question.
The only way to avoid having the players own mental ability extend into the game space is if the character is so removed from the choices of the player that it becomes an automaton. As long as the player makes choses on behalf of the player, or the player in any way animates the portrayal (that is, if the player role plays the character), then the player's mind is also in the game space.
And if the character really was separate from the player, so that you could say that it made choices without the input of the player, and its abilities did not depend on the players, then in what sense would you be actually playing the game much less the character?
or the game shouldn't have pretensions of allowing you to play characters with such qualities that are different from your own - no mental stats, just physical stats and maybe some sort of magical stats like 'mana' and RQ's "POWer." A game could limit itself to "your consciousness is projected into the body of a fantasy character in an alternate world" sort of narratives, for instance.
Again, what it should be is a fairly subjective statement, but I don't think this fact that the player's decision making ability and charisma extend into the game universe and become a part of it is a problem to be solved. And, I think most RPers - even if they've never articulated the issue fully - understand that you can't take them out of the game, and probably do not want to be taken out of the game (otherwise, why play), and yet are still also OK with playing something somewhat different than themselves and yet know at the same time that their character can never be fully distinct from themselves. This limitation is something you have to just live with if you want to play a traditional RPG. All traditional RPGs are subject to it, and I think you are correct that while we could go the other way and completely eliminate the separate 'mind' of the character, we can't in fact eliminate the mind of the player from the game space.
Whether we should eliminate the mind of the character completely is another matter.
I find that a lot of people - and this a very human thing to do - are perfectly comfortable reasoning on the basis of qualitative differences - "white/black", "light/dark". And most people are perfectly comfortable with reasoning on the basis of quantitative differences provided they can be demonstrated a tangible objective measurement. But, I find that most things in the real world don't exactly fall into either category. You can point out that "white" and "black" and "light" and "dark" are themselves quantitative differences that exist on a continuum, and while that is true you shouldn't get so caught up in that as to deny that those differences don't at some point become qualitative. Likewise, there are many things that exist on a continuum, where the means to objectively measure them are not at all obvious - yet the continuum is there nonetheless. The two extremes we are talking about - on the one hand the character as independent automaton where the mind of the player doesn't intrude into the game space, and on the other hand the character as complete extension of the player's consciousness without its own mental attributes, are radical extremes. There is in the middle a continuum of mixed approaches that are accepting of imperfection, and I think should be allowed to exist.