This kind of exists in Norway in the sense that we have at least two systems for communicating with government offices and, to some degree other organizations and people (haven't quite figured that out). This isn't an email solution as such though.

The thing is, all of these solutions are much maligned - despite being a lot better than what we had before (send/receive paper). If the state were to offer email accounts, people would complain about how bad they were (whether true or not) and argue that we should "let the market sort it out".

Which brings us to where we are now. With the market "sorting it out".