I'd much rather have a refined version of the gamertag, where you don't
have to always be known as the same thing in every game. (Though you would have the option to be, of course.) Personally, I'd rather adopt a different handle in different genres--different games--to suit my fancy, playstyle, or whatever. (Heck, I might just want to make a really bad pun somewhere and not have it follow me around forever.
)
It seems like a rather trivial thing to me to allow individual handles on games (which would not be allowed to duplicate unique gamertags) which you could turn on and off (or, say, only let people on your friends' list see through) to make it feel more customizable and personal with each of the games. (I hate using one name for everything. I don't do it in MMORPG's, so why would I want to do it in EVERY online game?)
Just so long as you don't lose out on the advantages of a central identity, I think different levels of "opting-in" is just plain better.