Fun fact: queen bees can be artificially inseminated, and most commercial queens are. Beekeepers prefer naturally-inseminated queens, because they're stronger, but "nature" can't keep up with commercial demand.

You're correct about "breeding more" not being trivial, but they do it on an industrial scale. In really broad strokes: in late winter, in preparation for pollination season, they feed their hives intensively (with sugar syrup) and add extra brood boxes for the queens to fill with eggs. Then they split the hives, leaving the old queen in one box, and adding new queens to the box(es) they take off. Voila! Double (or more) the hives.

Pollination is where commercial beekeepers earn their living, by renting out hives of bees to farmers. Honey production is not necessarily an afterthought, even though it doesn't really turn a profit - it's worth doing because you'll be putting the bees on nectar flows for the summer, anyway, so you won't have to feed them, and extracting (some of) the honey covers transportation costs - but all the money's in pollination.

I could keep going and going - queen production and hive splitting are fascinating topics on their own - but I'll stop before I risk boring people with an over-long comment. I have commercial beekeepers in my family, and I've worked (summer / vacation jobs, when I was a kid) every part of the process.

(This is all in a USA-ag context. Beekeeping is - very! - different in other parts of the world.)