Side note: Here's another kind of ridiculous service that I hear advertised on conservative talk radio: https://www.reagan.com/
Is this true? Is it possible, with current SMTP requirements? I'll give them the benefit of the doubt that they're not actively copying it for the purpose of keeping records they can give to someone else, or scanning it to insert ads.
But to act as a mail server, in my understanding of the state of the art, they need to take incoming mail in a format they can decrypt it - functionally equivalent to 'scanning' it. They need to store it on their servers - 'copy' it - so you can download it over POP3 (or IMAP, in which case it remains on the server).
I don't think it's possible to act as a no-knowledge mail server given current mail requirements without using PGP. And to do a bit of demographic analysis, the group of people who "Feel pride of owning an email address with Ronald Reagan's name" have a narrow intersection with the group of people familiar with PGP.
So the whole "private" thing is just baseless marketing.