Interestingly, DD has been dealing with plantar warts and we've been seeing a podiatrist, because home stuff wasn't working. He's been using something with the same acid as aspirin (I think), but stronger. Its working, hoorah!
But he also said that you don't technically have to treat every wart. The goal of the treatment is to irritate your skin so that your body will recognize the virus causing the warts as a virus/foreign. When it does, your body gets rid of all the warts, not only the one(s) you treated. He said it's faster to treat both of DDs warts though. If you had tons, they might treat the largest rather than all of them.
Totally mainstream doctor, but warts are apparently odd things in origin and treatment goals.