We've never had a candidate do 10 on-sites nor would we encourage someone to. That'd indeed be incredibly exhausting. We encourage them to be broad with the number of companies they do an initial pitch call with, then be selective about who they move forward with to an on-site.
Wow. Do you actually find that less than 10 on-sites is sufficient to obtain at least one offer? A >10% success rate seems very high to me, even with the vetting you provide. Admittedly I have only anecdotal data.