While I don’t disagree with you in principle, I do find it a bit funny that you’ve picked one of the easiest services to change between as your hill.
There’s no reason you _ have_ to use Gmail, or Hotmail. There are a billion email providers and if you have enough technical knowledge, you can even run your own (I really don’t recommend this though, it’s harder then it seems to do it safely and securely).
If you pick a provider outside the US, your government can’t do dick about getting it shut down, and if you pick one in a particularly privacy-conscious country, you can have everything encrypted to the point where the provider themselves can’t read your messages.
Also, I assume this is similar in the States, but I’ve seen government IT projects in the UK and some of them are truly awful. I wouldn’t necessarily trust them to look after important emails for me. Plus a single source of email would be an awfully tempting target for hacker groups around the world.