Response time isn't zero, though. Likely the attacker would be long gone before these people show up.

I agree it's unpleasant being physically assaulted on the street (happened to me 8 years ago and I still think about it often), as is the utter lack of interest from the police in helping in such situations, but I don't think a private security force is going to do much better.

And to your other point, there is already a thing for tracking someone down after the fact if the police aren't helpful: private investigators.