I assume there's a procedure that you could use to report a particular taxi car/driver, which would put them in a world of hurt for cheating. That's another reason why it's good to have a trustworthy third party there.
There is, at least in theory: call 311. However what's to stop the driver from slowing the meter down before he gets inspected? There's no GPS in the meter, as far as I'm aware, so I don't believe there's a way to truly audit the fares the driver has already taken.
They should, and perhaps that's improved in recent years, but it was definitely a common problem as few as 3-4 years ago (from my experience, I've largely switched away from yellow cabs to Uber/Lyft - mostly because the price and experience are vastly more consistent)
I have a coworker who reported fraudulent cab driver activity to the TLC. It was an arduous process involving multiple interviews and a hearing, and in the end the driver was fined about $200. Nothing inherently unfair about that process, but it's hardly a world of hurt.