Emails controlled by the government? No, never. Emails are a decentralized protocol and there is no point what so ever to have the government controlling it. Look, emails are not safe, not encrypted. See all emails as public knowledge. If I go to their website and login to view sensitive information about me, then it is safer. Apps are optional.
If you are talking about Kivra then there are private companies alternatives as well. You as a user pick and choose. Personally I dont use it as I get like one letter per year and would forget to login to it. There are better alternatives for normal letters as well.
Many do not run their own email server. It is just too hard. Companies choose Microsoft or Gmail to host email as it is cheap for them or included in something like office 365. Google have admitted that they read users’ email in search for custom advertisement. I would assume the same is true for Microsoft. On the inside we just have to trust them that they don’t make too many copies to foreign power or abuse it in any other way.
On the private side(not companies), Gmail really dominate. Very many don’t even know what selfhosting is and even fewer have the know-how and actually do it for email. People just don’t want that burden of selfhosting, maintenance, work. I would love the world to get more decentralized, use peer to peer, but today everything is more centralized than ever before.
Email should be E2EE, but that is never going to happen without the big players on that train - they just have too huge market share and that would go against their profitability.