It's unpleasant to be physically assaulted, and I'd like to avoid it in the future.
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.
What you want is the ability to pay to get expedited help, to which I say is that the fair option to those who can't afford to pay for protection?
Ideally everyone would be protected from random attacks on the street, not just those able to pay.
Exactly. You are advocating for a paid service, some sort of commercial company to do the enforcement. How do you think they'd generate revenue otherwise? Currently San Francisco is setup that way, you pay private security because the cops are useless. That's not like that everywhere. You should fix your police, not bandaid fix the problem for the people who can afford it while leaving the people who can't to suffer.