There's an inherit assumption that people would rather build loyalty to people over companies for specific services and its unclear if that's true. A perfect counter example to your cleaning example is Homejoy.
You can still build loyalty to both the middleman and the service provider at the same time this way for many services - I will stick with Homejoy because I like the ease of not dealing with cash/checks and phone scheduling.
The situation for Uber is that Uber's business model has nothing to offer to people that want to schedule a specific driver, rather than a convenient pickup at a good price.
I get my haircut by the same person every single time not because I think they are the best hair-cutter in the world but because I don't have to explain to them how I like it, they already know and I know they can do it that way, so going to them eliminates 5-10 minutes of explanation and a lot of uncertainty as to what the end result will look like.
For the same reasons I agree with crazypyro that "Uber for Massages" (local massages being something people tend to find one provider and stick with them for consistency) is not nearly as compelling as Uber for transportation where all I care is that the driver gets me to where I'm going in a relatively short timeframe and relatively safely.
I've heard a lot of "HomeJoy is meh but they are cheap. "