I'd be surprised were it legal to have the police drag someone out of a room they've paid for and been checked into, merely because another guest wants that room.

Sure, you can ask, but on what legal basis do you have to apply violence?

The hotel is private property. If the owners of the property ask you to leave and you don't, you are trespassing.

I doubt it's quite that simple. It's private property that serves the public. We've had court rulings saying you can't, e.g., refuse to rent your wedding venue to gay couples. If you make accommodations available to the public, there are legal responsibilities that go along with that.

I don't know what the specific regulations are surrounding hotel rooms, but certainly they're not "private property" in the same way that your house is.

These aren't just bums off the street. You signed a contract with the airline or hotel. You haven't violated the contract by making too much noise, or selling dope out of the room. I don't think your argument is valid, but IANAL.

This is incorrect. In a hotel, much like in an apartment, there are significant legal protections for tenants have paid and not violated any laws.

Errors happen, of course, but has a hotel customer even been removed from a room post-check-in because a member of staff needs the room?

Edit: From a major chain at least. I'm sure all manner of poor decisions have been made by smaller/single location operators, though they aren't really comparable to United.