As for simply delivering them to other directories: that’s pretty easy depending on what very agent you use (Postfix, qmail, sendmail etc). They are all designed to support that. It’s the clients that struggle.
At the time I was only experimenting with it for an idea I never fully realized, creating a system for video games to automatically play games asynchronously using email instead of a server (also you could see it was your turn again just by email notifications), thus being able to survive in perpetuity as long as SMTP remained a thing, but I could see using it to do what you're suggesting as well.
I run my own server so info stuff like this automatically as the mail comes in.
The people saying “use smtp” don’t know what they are talking about: SMTP is the protocol for delivering mail to a host. You want to process the message as or after it arrives.