I have never heard of a cougar being hit by a car. I just don't see a car sneaking up on a cougar.
I do however agree that they aren't a real threat to most people. A healthy cougar will avoid humans, generally. I camped in a tent immediately after a cougar sighting. I was still more worried about a curious bear looking for food.
I think cougars scare people because they are large, basically invisible, extremely effective ambush predators. They will attack and kill pets and infants. Joggers also seem to trigger their predatory responses.
That is understandably terrifying. One of the few cases where a cougar needs to be destroyed is when it has lost its fear of people. Very rare, but very bad for the other people and cougars in the area.
I think education can go a long way. They are not evil baby eaters, they are beautiful animals with predictable predator responses. If you see one, don't try and run away! Maybe reconsider that solo wilderness jog with earbuds.
Even with cougars there are some problems, with actual lions they would need to be constantly tracked, sedated and relocated.
https://www.tricitynews.com/news/cougar-warning-issued-to-be...
https://bc.ctvnews.ca/coquitlam-cougar-sighting-residents-ad...
https://www.nsnews.com/news/north-van-cougar-sightings-promp...
Lions are everywhere in some parts of Vancouver. It is rare that one must actually be put down. We can get along.
Best thing for keeping everyone alive:
https://www.mec.ca/en/product/4007-144/Bear-Bangers-%286-Pac...