The main issue is memory required to store all this historical information. I haven't a clue how many servers there are, but daily I see 10m+ players online. If everyone has at least 11 players required to play (the minimum), this is 110m player profiles

Now consider just the games played, goals, assists, average rating for these 110m players for a single season. Including headings you're talking about 18 bytes required minimum for a single seasons stat. This equates to 2GB of extra memory (storage) required.

Actually looking at it like that, it's not that bad an idea and not beyond the realms of possibility.