The varroa mite has been pretty effective at removing them so far. Today honeybees are essentially livestock, to the point where any given bee you see is very likely owned by someone.

I can't find any data to back that up. On the contrary, it seems there's about 1.4 colonies per square mile in the U.S. Varroa has not been an existential threat to feral honeybees, and almost certainly has hit them much less hard than commercial honeybees because feral honeybees swarm much more often, which means they reproduce more often (thus get to adapt faster) and abandon old comb more often (which helps fight lots of diseases).