>Seems to me that no treatment beekeepers don't mind letting mites kill bees
I haven't had a problem with Varroa for a decade now. Mites aren't killing my bees. Of course we mind if our bees are dying. That doesn't mean that the best course of action is to do something even if it's wrong.
In reality our actions often have the opposite effect of what we expect. When people decided to poison the prairie dogs to get less prairie dogs, the results were quite the opposite. They poisoned some prairie dogs, to be sure, but the end result was less of all of their predators (black footed ferrets, burrowing owls, rattle snakes, hawks, eagles, coyotes...) resulting in a population explosion of prairie dogs. Many things, including treating for mites, are like this in that the result is not what you thought you were doing directly. The secondary effects come back to haunt you.
What species would be affected if varroa were somehow eradicated?
"Ve are too soon olt und too late schmart."- A nameless German philosopher