Along the same lines, a Gmail-esque Thunderbird web service would be amazing. I could finally de-google myself completely if that were the case.

Currently, I need to set up my own email hosting through a service like fastmail and then configure a desktop client(like Thuderbird) to use it.

A Mozilla Gmail-esque service would remove a lot of the friction there and probably bring in a bunch of users who are tired of google running everything.