Well, mutt is close to what you say. It's just a MUA [1].

That is, it just reads emails on a local mailfolder. Fetching emails to that mailfolder from the server, sending emails and doing other operations is a task of 3rd party programs.

[1] OK, it has a few addons for lazy people. But most experienced users ignore them.

That's what mutt is. You can compile it with support for imap and smtp, and most packaged versions of it are built that way, but the traditional way of using it is just as way of reading and sorting emails. Fetching emails from the server is done by a POP or IMAP agent (I use offlineimap), sending mail is handled by an smtp agent (I use msmtp), composing emails is done with $EDITOR.

I don't think that mutt is the most unix-philosophy-aligned MUA possible, it feels kind of like GNU tools: unixy, but jam packed with too many flags and options and convenience features. The unix philosophy would prefer that the application's design be changed to better accomodate implementing those extra features externally where plausible. But the perfect unix MUA would do the same things as mutt.

Actually, the traditional way (that still works perfectly fine, actually) is to not "fetch emails" at all. You simply have an SMTP server on your machine and have it either be the MX for your domain or have the MX forward emails for your address(es) to your machine via SMTP, and then have the MTA deliver to the mailbox file or directory that Mutt reads from.

I think a lot of Mutt users do what you are describing.

I use mbsync to synchronize my mail over IMAP with my remote mailserver. I use mu to index it for search. I use msmtp to send mail. And I use mutt to read and write mail.

I didn't know, thank you everyone!