I have to disagree that this is "exactly how normal taxis work". Notable differences (many apply to Uber/Lyft also):
1) There's no check to ensure that the vehicle is ensured for commercial rides before they start taking hails.
2) Likewise, no background check.
3) No regulatory body to investigate cases of e.g. scamming passengers out of money or refusal to comply with agreed-upon rates and dropoff. [1]
4) The local PD doesn't stand ready to treat assault on a driver like assault on a police officer, in terms of marshalling resources.
5) No central registry, or even private registry of cars/drivers in operation.
6) Drivers aren't trained in the relevant anti-robbery countermeasures.
7) In NYC, the barrier to prevent the most obvious kinds of robbery.
That makes a big difference in safety of paying cash to a roving operator!
Sadly, I think the "big corp middleman" does add a lot of value that a free app can't replicate without similar investment, scale, and "walled garden"-ness.
[1] I know commenters here like to roll their eyes about the clumsiness and lackadaisical enforcement -- I'm one of them! But it's at least something, which prevents a major scale-up of this behavior.