I haven't played a lot of Street Fighter 4 on my PS3, but I hear that there are certain things you can achieve in the game that will unlock an item in Home. The one in particular I saw was someone winning some online matches with Dan, and he got a Dan-themed T-shirt in Home.

Even if one doesn't care about Home, or the trophies, at least getting *something* gives it a little more value.

As far as achievements/trophies go, it's probably good for other people to see them so they know what you've done in the game. Like, if you want to talk to a friend about something in a game but you don't know if they've done it yet (and don't want to spoil it), you can take a peek at their progress. In a sense, the achievements/trophies can give someone a nudge when they think they've finished a game and see that there's other stuff that they can do or play around with. Just adds a little more value to the game experience that you can ignore completely.