Unrelated but made me think of this anecdote; Many years ago I met a tech-savy captain who did have satellite internet on his ship, but it was incredibly expensive (not sure about current pricing), so he only used it briefly every now and then. To receive e-mails (and some other things) he had a server somewhere which fetches everything and then zips it up as compressed as possible and when online synced it to a local computer/server that's onboard.

It was pretty fun/interesting to see creative solutions like that to deal with very limited bandwidth in practice.

This is what I do, usually... I run my own mailserver, but I also have a gmail account, and I just use Thunderbird to connect to both... when I'm on desktop. I auto-download and auto-delete the mail from gmail server, in order to stay under their storage limit. But that can end up using quite a bit of bandwidth, and unexpected delays if some uncle sends me some giant mp4 cat video. The alternative would be having to periodically go in and download everything and clean out my gmail, which is just too irritating.

Depends on your workflow. You might just mark everything as read, or archive them, rather than download and read them.