I agree, the setting might be confusing on the website then. App-only would definitely be the preferred way.
I do it similarly nowadays. I add all the songs mostly via the website and add the tempo and set the font size during the next rehearsal. As you state: The pinch-zoom is rather quickly done and saved.
However, if there was an auto-fit/non-wrap in the app, it might be more convenient as I set the font size on my device. The other users have the same font size then I think? Also it's the same on phones, etc.
So such an option would ease the font size topic on each device automatically, if that's wanted. I imagine it as a separate button or multi-finger gesture to toggle on the auto-fit, similarly to showing the chords. Then it would be switched between auto-fit and personal setting, if there is any.