Ah yes, a government owned email service, what could go wrong?
It makes no sense that in the physical world, we entrust government with identity verification and transmitting correspondence, but that trust is somehow lost in the digital world.
Each US citizen deserves access to a public network to express their First Amendment right without moderation.
Sure, make access to the internet an inalienable right also, but web hosting and domains are cheap enough that that should suffice. The network is the internet, and if people want to visit your website to see what you are saying, they can.
Now, of course, you shouldn't be organizing a criminal conspiracy or in general much anti-government protests over the mail or government-downed email. But the majority of communication is quite benign, and so having a government email for the 80% use case (bills, party invites, holiday wishes, etc) would be great. You can use a separate service for your more sensitive communication.
The reality is that it is about as exciting as getting your paper postal mail delivered in your physical mailbox.