My story:
For many years I happily used pop3 with K-9 mail on my phone only. Yes, thats usually means only copy of mail was on phone. Not ideal.
Now, when google will soon effectively dont offer free mails with custom domains I started to look for options (and found them).
But to move to my new email provider I wanted to backup my mails and I could not fully do it, becouse mostly they are on my pop3 acc in phone with k-9 mail. And k-9 mail does not offer backup option (serious drawback I would say… how hard it would be to allow create .mbox file for everything?). Sure I can re-send them to myself but thats hassle.
Anyway, after thinking how to do it better in future I ended up with this strategy:
My main email checking/replying/deleting option on phone will be IMAP, but also same mail accounts will be set on phone as POP3 (with manual push + leave on server option) + also POP3 (with leave on server) on 1-2 desktop machines on same accounts.
So I will use IMAP for checking e-mail, replying, deleting un-needed and POP3 just as backup (local storage).
When my email box will be near full I will delete e-mail from server using webmail or IMAP. Sure I can pay more (or find free options) to never run out of space, but thats not really neccesarily I think.