> doesn’t work offline on mobile devices

To some degree, that isn't true anymore as of last week but of course, you meant when you used it, not generally: https://www.fastmail.com/blog/offline-in-beta/

Oh so some of it works offline.

Useless to me. Seriously.

I write a lot of email on planes and do a lot of email management.

All that works on the default Apple stuff as shipped other than account management. Using IMAP and iCal etc.

Have you looked at their list of what doesn't work offline? It seems like it's mainly attachment management limitations than limitations of managing the emails themselves.