I remember one Super Bowl weekend trying to get home via cab from Tribeca after the game was over.
Looking down West Broadway, you could see multiple groups of people at each intersection with their arms up trying to get the first cab to go by.
Or during just times in general. When I first moved to NYC, I was my normal polite self when people would say "I hailed it first" and let them take the cab. After the fourth or fifth time this happened with cabs I was 90% I had hailed first, I realized you had to pretend to be some alpha male and shout "Get the F away from my cab!" in order to guarantee you got in the cab.
I don't know if anyone keeps stats on this but I would bet money that the number of fights in NYC due to the above must have gone down once Uber became common.
Not in NYC, but I've seen cab drivers auctioning rides by asking "who will pay more" after some events. At airports I've definitely had my share of drivers asking multiple passengers where they're going so they could go to the most advantageous location. Both were obviously illegal in the cities I was.
Remembering those, I can definitely see why everyone started using Uber.
You also have to discard the "customer is always right" mindset when using taxis in NYC.
It is notoriously difficult to convince a taxi to take you cross-town. The few times I succeeded... it was a mistake, a miserable experience and it would have been faster to walk.
Conceptually it would be nice to just be able to get a taxi from point A to point B, no questions asked, and sometimes when a driver doesn't want to do it it comes down to racism or profit, but other times it's because you're asking to do something that isn't actually a good idea.