On thinking some more, a lot of jobs (including driving) amount to “Operate the controls of a piece of machinery”. And nowadays, a lot of that machinery is computerized anyway, with the controls just being computer inputs. So it’d make a lot more sense for your “robot” to just connect to that computer that’s there anyway via Bluetooth or something, and “drive the car” without using its “hands” at all.
If, of course, there’s even any reason to not build the driver-unit directly into the car.
Yeah, by the time the technology advances that we have generic, standalone human robots, many of these use-cases will have long been solved. Driving a car is a prime example.
Robots are going to quickly be seen as tools, not replacement humans. Who wants or needs their microwave to look like a chef?
Unless they’re constructing skyscraper-sized vending machines which absorb and dispense cars, self- and valet-parking will continue to be performed by humans.
Now watch some doper link to a site where theyv’e already done that. 
Ask and ye shall receive:
These have been around for something like 15 years, maybe more. Invented in Japan, but now found elsewhere too.
I have seen those things for at least 25 years— they are just not necessarily “skyscraper-sized”.
Wikipedia has an article on automated parking systems.
I just learned about this on last night’s John Oliver: A Polish humanoid robot chasing feral pigs.
It’s not clear that the humanoid form is best, but I’ll bet he gets better results than chasing them with a Roomba.
His name is Edward Warchocki