One of the characteristics bee breeders look for is hygiene- more hygienic bees will remove more of their own mites. It’s not entirely dependent on the type of bee.

I don't really know the bee science, but a) our bees were just the generic European bees and b) the bees on sentinel duty at the hive entrance were pretty good at noticing whatever didn't belong. Varroa mites are very noticeable, especially at the bee scale.

That said, varroa absolutely could overwhelm a colony. Then you had to report it, burn the infected colonies and wait for the inspectors. Not fun.