What do you think an MTA, MDA, and mail stores are?

They're not really caches, they're storage infrastructure.

There is still a difference between cache and what's on hard disk.

Mmmm, RSS over e-mail. Is it bad that I want this?

I have been using https://github.com/rss2email/rss2email with a dedicated email address for several years now, tracking around a hundred RSS feeds.

The system works quite well, and I can read my RSS both via a client-side app (thunderbird in my case) and on the go via the webmail. I even made a small modification to rss2email to automatically "tag" the mails so I can use mail filters to automatically sorts the feeds into different folders.

I have a server that fetches the RSS content a few times a day, but I guess it could also work "locally", for example by doing it once each time I turn on my computer (if you are okay with "missing out" sometimes on very active feeds).

I decided to do the switch when I noted that the interfaces of my email client and of my RSS reader were basically indistinguishable.

EDIT: for the anecdote, this project was initially created by the very same Aaron Swartz that, among other things, contributed to the creation of the RSS format http://www.aaronsw.com/weblog/001148

There's quite a few services that will convert new items into emails for you (IFTTT, and others).

A lot of email clients also have support inbuilt. (Thunderbird, Outlook, and others).

To add to the other suggestions, 'blogtrottr' is a convenient free service for receiving RSS as email, with settings for frequency and so on.

Check out https://rssmailer.app

Isn't that just a mailing list?

I guess I need to clarify. I don't want email summaries of blogs - that would be awful. I want websites to offer the ability to send raw RSS feeds over email as a push service.

So basically WebSub but you don't need to run a WebSub server - you could just parse feeds using, for example, a procmail script. Email is already a well-supported protocol; WebSub is not.