I don't know, I think it's the way they've been done before that's gamey and rubbish, not the idea itself. To take it away from the restricting it to just killstreaks but more about achievements in general...
Imagine for example, you get a small achievement for making 5 kills AND landing safely. The landing safely part would take the gaminess out of it to some degree. Perhaps you could simply unlock a medal to put on your player model in the game.
Or an achievement for keeping every bomber alive from a whole bomber sortie (as long as there are enemy players on the server
).
There are lots of things that could be added that would be fun to achieve AND promote people playing in a sensible way.