It might indeed lead to more chases, but the chases would be awfully short. There is no reason to drive 100 miles an hour if no one is chasing you.
Besides that, beating someone to “a paste” doesn’t do anything to compensate innocent victims of a loss. As much as you want to talk tough about this, it’s not an answer. No one says, “Gee, a police car ran into me and now I’m crippled for life, but the policeman beat up the guy who led the high-speed chase, so I’m perfectly happy with how all this turned out. God Bless America!”
Moreover, as I noted before, with modern technology, like helicopters and sophisticated communications systems, I don’t think they would have the ability to “do as they please.” If anything, it would only delay punishment.
And the current methods of “sophisticated communication and helicopters” work so well today that every case is solved, and every stolen car is recovered, so we don’t need chases. I’m so glad to hear it.
As I wrote before, your “chase free zones” would be the same sorta invitation that school “gun free zones” are.