This has been suggested, and turned down, before. Although it would decrease the clutter it would also decrease the value of all the current icons.
Think of it as a real-life trophy cabinet. Which looks better, a cabinet full of trophies, or one trophy with a big number on it?
I would only see a problem if everyone had tons of icons. This is not the case currently because we have been pretty successful in limiting the number of icons given, plus icons "disappear" when users take breaks or quit.
I think that a better way to achieve a similar result would be to for example combine 5 small tournament icons into one big one. This way we could limit the number of icons, but the awesomeness would still be there in a form of a bigger icon.