Is an Archive Mailbox just a regular mailbox? Or is it special?
The computer can track thousands upon thousands of messages no matter what mailbox, so you are right - this is purely a human affordance.

Setting aside any other mail service (since this is about Apple) - the archive is there purely to be a quick parking place for a message you don’t want cluttering your inbox. Most people that have used mail for a while will decide that inbox zero is a good thing so you need a place to move messages you’re not ready to decide to reply / delete or file.

There’s nothing fancy about archive - it’s purgatory for messages and I wouldn’t use it unless you find it helps you out organizationally. I think the list of premises you have stated seem to line up and you’re not missing anything special or dramatic about this topic or the design of Apple mail app.