Hm, I'm personally down for this kind of stuff to be present in most games.
For one, ye, this is basically adding a better way to showoff and helping out with "bragging rights".
But the additional benefit is to provide a side challenge for more groups of people. Other games (especially the MMO scene) have shown how much of a "main goal"
collecting achievements is for a good big bunch of people.
I'm personally not the overachiever-type-of-player, nor a completionist but on the other hand I really try hard when it comes to the most unobtainable achievements in, that take a loooooong time to complete (Quality over Quantity is where I'm at lol). The satisfaction to unlock the thing in the end is just superb. So, yeah I'm a representative of this sub-group of "achievement hunters" hehe. Naturally I'd love to be able to showoff those hard-to-get achievements, even passively so, through someone simply inspecting my profile.
I should try to sit down and think of some achievement ideas of my own.