The problem is that the Dutch government bought the whole 'free market will solves every problem' ideology. So obviously, a city government was not allowed to mandate anything in this context.
Public transport is the public good that the government pays (in part) for. I doubt that you can randomly pay taxis to be available at night. Then you have to figure out a scheme who gets paid and who doesn't. Otherwise, you may find lots of people who want to get paid for doing nothing at night.
I don't know the details of the old taxi system. There were a limited number of licenses. There was a limit on how much a taxi could charge. But probably there were lots of other requirements as well.
Public transport is the public good that the government pays (in part) for. I doubt that you can randomly pay taxis to be available at night. Then you have to figure out a scheme who gets paid and who doesn't. Otherwise, you may find lots of people who want to get paid for doing nothing at night.
I don't know the details of the old taxi system. There were a limited number of licenses. There was a limit on how much a taxi could charge. But probably there were lots of other requirements as well.