I don't buy or play games for the story, most of the time, unless I really love the world or franchise or fantasy involved.
I have gone out of my way to find difficult and challenging games because they give me the most satisfaction, but many, many boss fights leave me disappointed either way.
I certainly love being the hero, but it really depends on my mood. Honestly, I wish that Twilight Princess had difficulty settings, that Fallout 3 wasn't incredibly easy, that some actual skill was required to complete Kingdom Hearts II.
Granted, all of these games have optional areas to cater to the crowd looking for challenging combat (cave of ordeals, a few sidequests, that 50-round paradox cup...), but it doesn't really feel the same as beating a game with a challenging boss.
It depends what you call "skilled player," really, because when I think of games I want to play for skill, they involve strategy or reflexes, one of the two. Heroism can involve these too, but it doesn't seem to in most games. Granted, I think it'd be unfair if a boss fight was incredibly difficult, because players would have to be of a certain caliber to complete a game, leaving others who were interested simply unable to do it.
Personally, although I like RTS games and tactical combat games, and I love shooters like Ikaruga, when it comes to boss fights, I want the heroic ordeal, even if it does make me feel mediocre afterwards, because I know I'd feel even worse if it took me 30 tries.
If I'm a "skilled" player, I'd be looking for that type of competitive gameplay the whole time, and I'd easily settle for a boss fight that made me feel like a winner rather than another section of the game that's nearly impossible to complete.