The trouble with picking up rocks is you have to bend down. The moment you do that, you look a lot smaller and that’s when they will attack (so I’ve read).
I haven’t tested that hypothesis, though. When I’m hiking in cougar territory I carry a big club or rocks. Pick them up before you need them. I think most people are unprepared for the ferocity and violence of a big cat attack and sticks and rocks may be useless. They also hit you hard and try to snap your neck, so you don’t have time to use them.