Hmm. I think the idea of 'want your character to succeed' is an idea that contains an awful lot of individual differences from game to game. Especially when RPGs usually lack a specific win condition overall, at which point the notion of success gets a lot fuzzier.
Depends on scale, too.
In any moment of play it's fairly safe to assume I (and, I'd expect, nearly all players nearly all of the time) want my character to succeed in whatever it happens to be doing in that moment, otherwise I wouldn't have the character doing it.
From there, the scale broadens:
--- short-term success on a given mission, heist, or adventure;
--- medium-term success in accumulating wealth, reputation, levels, or other ongoing reward(s);
--- long-term success in achieving whatever in-fiction life goals (if any) the character might have.
Achieving the latter of those, at or near the end of a campaign, might well be seen as an overall win condition. Different tables, and even different players at the same table, put more or less emphasis on each of those scales of success, though, thus the "individual differences" to which you refer.