Archiving mail in a local mailbox

I believe one could create an Automator workflow to achieve what you seek but this requires AppleScript knowledge, which I lack.

There are a few knowledgeable contributors on the Communities that could help, though. If you want to pursue this avenue, please post a brand new question specific to that topic so that those expert contributors see it.

It might work the 1st time you do it but after that, dragging the same folder to “On My Mac” would probably create a new folder. You’d then have 2 folders in “On My Mac.”

I wonder if a 3rd party solution like MailBackupX wouldn’t be a better solution.

When it comes to emails on a Mac, using the cloud or not is not an issue: all the emails are downloaded to the Mac and thus are part of a Time Machine backup. The sticky point is that it’s not easy (read near impractical) to recover individual emails from a Time Machine backup since macOS Catalina. I would not recommend this avenue.

On a Mac you could implement a Mail rule to move the new emails to a folder in the “On My Mac” location. The emails would then only be stored on the Mac.

No, sorry, Mail rules can’t. You could still do it manually, though, by selecting a range of emails and moving them to a folder in the “On My Mac” location.