You're missing that some tourist taxes are taxes on the hotel room, whereas others are on the tourist - and the hotel has been asked to collect it on the behalf of the local govt (as I know is the case for Frankfurt, for example). So would a hotel get in trouble if they were to subsidise tourists and pay their tax for them? Probably not, if we're being honest. I'm sure nobody has ever tried - no hotel chain in any of these cities we're talking about.

Is it a different thing to expect a hotel to pay what is in effect an entry fee to an area vs. a tax applied on a room rate which is really a type of targeted VAT? Yes.