If one wants to be able to access one's e-mail across devices and to be able to set up an existing account under a new e-mail client and have all the mail associated with it "just be there" then using the two existing protocols that do that, IMAP (generic and more common) or Microsoft Exchange is the way to go.
There's no muss, no fuss. The e-mail client is just exactly that, a client, with local copies of a certain number of the most recent messages and their message bodies kept so they can be accessed if you're offline, but where all messages are permanently stored on the e-mail server. Folders are also created and stored on the server.
You can, of course, create copies of things in your IMAP folders in local folders as well, but I've never yet found a reason to do so.
One of the reasons IMAP came into existence was the recognition that people were increasingly going to need to have seamless access to their e-mail across devices and platforms, and to be able to change computers, e-mail clients, etc., with ease. It's now been around way more than long enough to prove that it does exactly what it was set out to do.