The difference with Uber is that it requires a lot more trust to give someone access to your home while you're away to clean it. Not sure I would want to subscribe to a service where I would have to trust any local dude to visit my home. It's like a nanny. Picking someone to look after your kid is a very personal thing. It's not a lowest bidder thing.
Getting in a car is pretty much the most dangerous thing a person does in an average day. You may be trusting a cleaner with you possessions, but you're trusting that Uber driver with your life.
With a house cleaner, my desire to keep my possessions is at odds with the cleaner's desire to have more stuff. I have to count on their desire for repeat business, or their morality, to outweigh that.