I guess you assume that since your girl Sophie doesnt pay taxes that no housecleaner pay taxes?? Thats seems like an odd assumption.
One of my girlfriends cleans houses here in NH. She gets between 20.00-30.00 an hour for cleaning depending on what she is doing. She does pay taxes and brings all of her cleaning supplies. She has more people that want her to clean than she has time for!
Off topic, but many, many years ago, I babysat a couple children here at my home. I paid taxes on my meager wage. Not all independent workers don't pay taxes. Of course many don't, but not all!