I literally switched on "Enable offline support", caching "All mail" offline on my iPhone a few months ago. Tons of free space, only using 4GB for offline.

But when my phone is actually offline (on a plane or elevator) it beachballs when trying to find something.

(I work for Fastmail). That sounds odd – have you contacted our support team so we can look into it? https://www.fastmail.com/support/

I didn't, but I'll do so now. I usually don't bother with support, because I forget that good companies like Fastmail actually have a competent support team.

Not OP, but I had to change the mail cache from all mail to recent, I think because it couldn't handle how much mail I had? It would often get stuck not syncing, and offline would be unreliable and showing a blank screen. Recent works fine, but it would be worthwhile folks testing more with all mail enabled, especially if they have larger inboxes.

The mobile client now supports viewing emails offline.

Even desktop app on Linux and a web app.

Offline support was added in August last year: https://www.fastmail.com/blog/fastmail-works-offline/