I did my applications last year for Physics/Astronomy (theory).
4 applications, Oxbridge and 2 in Australia. Most programs only needed 3 LORs, but Rhodes required 6 (3 non-academic) and Gates-Cambridge 4 (1 non-academic). I started out with 8 planned apps, but it was too much effort and not really worth it, so I cut back to 4.
I had one first-author pub in the field and the University Medal (plus everything associated with that). I think if my apps had been less secure I would have done more, can’t imagine doing 22 though. 8-10 would have been my absolute limit! After all, you can only accept one offer.