Ah, I see now. This strikes me as an idea that people will like, but I just can't see the use case.
Maybe it's because I've never understood the whole "achievement" thing anyway, but I can't come up with a reason to care about them at all. I can't think of a reason to use a system that restricts access only to people with completely arbitrary credentials. I can't think of a reason to implement such a restriction, either.
I can think of a reason NOT to export my application's "badges" to other applications, if any: it would encourage people to create accounts on my system for the sole purpose of gaining these badges. It further encourages behavior designed to obtain badges.
That said, I don't want to be too down on the idea. It's got some potential as an information hub. I would consider losing the "badge"/"achievement" terminology, downplay the "access control" angle, and bill it as a more generic hub for sharing information about what users get done in a given application.
I could see benefit of sharing information about -- say -- how often a user makes posts on user-moderated discussions, as opposed to voting, or that sort of thing. Swapping numbers and ratios instead of boolean data reduces the arbitrariness of the thing. The ability to use them in subtle ways, as opposed to ham-fisted restrictions, would likewise reduce the temptation to create throw-away accounts.