I think some games can, but I don't know if that's a product of the system or the people. My Apocalypse World and Burning Wheel, FATE, Dogs... they all tend to the gritty and streetwise. It's why I want to run The Veil - cyberpunk is a natural genre for my style, and Gibson one of my favourite authors.I think, though, that some systems can be more demanding on the players than others, and challenging in that sense. To give examples: Prince Valiant and MHRP tend to be relatively light-hearted in the situations they throw up; whereas Burning Wheel (and I suspect Apocalypse World) can be much "heavier"/"deeper" (I'm not sure what the right word is).
Both are fun, but the latter is more likely to leave a participant feeling drained than is the former.
So my Prince Valiant might be a shade or two darker than yours, your Apocalypse World lighter than mine. I may push a character real hard at points where you'd ease off, and vice versa. But these are aesthetic choices.
Within that spectrum I maintain that it is important for players to feel relaxed, entertained, at ease. A creative experience can be a draining one, but it can just as easily be euphoric or invigorating.
Personally, I think these emotional responses are more about the authenticity brought by the players than anything system-specific. [MENTION=16586]Campbell[/MENTION] often talks about this quality of play, the integrity of the characterisation. I tend to assume it, but he's right to highlight the importance of it in character-driven play, which is where the challenge to character concept that you asked about is really located.