If only HO paid, then they are paying for you to provide a service. Then it is not an equal exchange.
If you’d rather sit as a business, go ahead but that is really a different model than THS which combines travel with sitting. I personally wouldn’t book a paid sitter who had to travel to me and would be sightseeing while staying at my home; if I paid a sitter I would hire someone local in my community, and then it would be providing a service not staying as a tourist as part of an exchange.