Save statistics across computers

I recently got a new computer, and was mildly upset to realize the statistics from my previous computer (blocks placed, time played, etc) were not saved even though I used the same Mojang account to log in. Being able to carry my statistics with me anywhere I log in would be a nice touch, and would make this page actually mean something to people like me who have played the game for many years on many different computers.

Not sure what topic to file this under, so I'll put it in UI. This is really more of a UX suggestion in my mind, but the topics are at least closely related.