https://en.wikipedia.org/wiki/Helicopter-based_hunting_in_Fi...
The people decided it was better to live with mountain lions instead of killing them off in 1990, after we killed off the grizzly and the wolf in the state. http://leginfo.legislature.ca.gov/faces/billNavClient.xhtml?...
Mountain lions (at least the ones evolved when we hunted them for the last 12,000 years) are much less hazardous to humans than grizzlies or wolf packs.
https://www.nytimes.com/2015/03/08/nyregion/that-howling-jus...
This limits hunting to public lands, of which, there might be 2-3 within an hour drive of the city. So no matter how much the hunters kill, they aren't likely to effect the populations in the surrounding suburbs.
There are more hunting spots in the rural areas, but those areas are also populated by natural hunters, like wild dogs and large cats.
It makes me very sad to go south and see the huge numbers of roadkills on the side of the highway. Where I'm from, we try real hard to inflate the deer population, since the winters and the coydogs keep the population down so much that the hunting isn't real easy.