All this time, the agency is taking a % cut for providing the original cleaner. After that, the additional value they add is zero.
So yes, it may be unethical to disintermediate the agency, but by this time you have been working with the cleaner for weeks/months, so you get a fairly good idea as to what sort of person they are.
It's interesting, there seems to be a few here on HN that have a problem with people building businesses and making money. Is it implausible that the cleaner you have had for months/years could end up with more work than they can handle and begin to bring in help to do the jobs they won? That's often how small businesses are created.
I am just saying the flaws in the business model as I've experienced it. Agencies could add value via insurance, holiday cover etc, but the ones I've experienced never do.