Yes, for sure. I've had professional home cleaners for nearly 10 years now. And over the course of those years, I've had many conversations with friends and neighbors who do as well (e.g. in giving/receiving recommendations). I can't imagine using a service that sends someone different every time, or even someone for whom I can't see reviews and receive references before the first visit. I think most of the people I've talked to are in the same boat. This is a service that requires putting a lot of trust in the service provider. I could potentially see myself using an app that helped me find a provider, but it would need to give me a lot of information about them up front, and let me choose from several. And then it would have to let me keep getting the same person every time. It ends up being more like an Angie's List than a Homejoy.
For something like a handyman, where the service is less intimate and less frequent, this might make more sense (though I have had enough horrible experiences with handymen that I also would want personal recommendations at this point)...