I believe taverns will be quite lucrative. It's no coincidence that taverns are the second building needed to grow a settlement from hamlet to village. Just one step behind a source of water! Taverns are often the beating heart of a city.
For players on long journeys, I expect they would want to stop at the local tavern/inn for room and board, stocking up on supplies and food. It is also a good place to gather information and in many games, a place where quests can be initiated.
I would expect a steady stream of income, especially for larger settlements, travel hubs and renowned taverns.
Can they be destroyed? Yes they can but I expect the repurcussions would be quite stiff for the perpetrator. Taverns are often inside a settlement with guards and sheriffs. I imagine that the aristocracy and nobles responsible for the settlement would also not be pleased. More importantly they can be rebuilt.