Wait, I live in the Netherlands and I wasn't even aware that Uber was around. Didn't they get banned years ago, with only Uber Black being allowed?
Usually they have a taxi sign on top of the car, and always have blue license plates (which you can only get if you are a taxi).
So, I think that the workaround must have been that they actually employ licensed taxi drivers. This is, however, only speculation.
Methinks the flexibility of dealing with temporary workers is more pertinent than the added cost. Pure speculation of course.
So all Uber drivers are taxi drivers and all Uber vehicles are taxi vehicles. Simple.
If Uber tried to somehow do taxi services without their drivers having taxi drivers licenses or their cars being registred taxi cars, they'd be laughed at.
Everything is really really simple once there is no taxi monopoly or medallion system.
I think it's always a regular taxi that shows up, though.
But then again I never take taxis either. For me it's either walk, bike or OV. It might be like that for you as well, which is why you forgot they exist.
Real world example - taking Uber to my workplace would cost me one-two hours of net pay, and I'm in the top 5% earners. Another one-two hours of net pay to go back home.
For comparison - public transportation costs 3€/day regardless of usage, and only takes about 15% longer to get there.