I did my Canadian Driver's license test in a Hertz Rental Car. I was a President's Circle Member and got upgraded to a Jaguar S-Type. It did not have a manual hand break - so of course at some point the parallel parking exercise came: I stopped the car. Turned off the engine.

Tester: Are you forgetting something?
Me: No
Tester: You sure?
Me: Yes - there is no manual hand break.
Tester: OK - I usually don't get to test in fancy cars

Anyhow - while I don't know about now - and not about California - it wasn't an issue at all back then in Ontario.