It is rare. The reason Uber and Lyft don’t have the same “work outside the network” problem that Wag / Airbnb does is because when you want a ride you want it now. If you had to wait for your “personal” driver to free up, you’d be waiting... or have to deal with scheduling in advance.

You schedule dog walks and lodging in advance, so it is quite tempting to cut the middle man out once you find what you like. Not so with transportation.