(ok mostly one game)
HQ?
For a pure adventure game, it makes sense that the player should be able to do what's practical for the player character. Of course, with all games, the designer chooses all the possible actions the player character can do, so players are limited to whatever the designer chose to allow.
In a way, this extends to RPG/Adventures, within reason. I know that it is entirely possible to get max skill in strength as a sorceress/rogue, but it doesn't really make sense for those characters to go bashing down doors - my opinion is that it would be out of character for a role-playing game where you are playing a certain type of character.
If the game is designed well, you wouldn't end up being stuck/unable to progress just because you didn't have X skill. That would be poor game design. In real life, some skills might take months before you even begin to become competent at it (e.g. picking locks/throwing accurately/climbing/sneaking/even fast talking). In a way, with HQ, a single point in a skill probably indicates minimum competency, and from there, it becomes more of a matter of how good you really are. So unless the heroine studied several years learning how to harness magic, I wouldn't expect that skill to be learnt in game.
Around other RPGs, that is, Action RPGs, I would really expect my characters to solely specialize in one area. Mostly because of the way these other RPGs have certain armor/equipments which need to be optimized to get the best firepower for your character, and in terms of skills (of the very few RPGs I've played), you don't really get to cross-class in most games anyway.
With QFI, which plays more like an adventure, I *think* you can still use other class solutions for dealing with things (at least, in some cases). But unlike HQ, QFI doesn't have up front hybridizing because of the way 'choose your character' works. Still, I need to play more before I can say anything definitive; Bt could give a better idea