They pass the collected taxes onto the government, and probably have the same opinion on hotel taxes as a retail shop would have on sales tax - it would boost business somewhat, if it were lower, but oh well.

From personal anecdotal experience, when traveling alone for short term, chain hotels are frequently cheaper than AirBnB - the host has to hit you up with cleaning fee per stay, while a large hotel has economies of scale working in its favor as far as cleaning, parking, utility bills and other stuff.