You are correct, mostly. UberPOP (which directly competed with taxi's) has been outlawed. The more expensive UberX has not. There's also UberBLACK, but that's more for business people.

What's really sorely needed is Uber outside of the Randstand region though. Taxi's are even more of a monopoly there so for consumers it's either pay up or get fucked, which results in horrible customer experiences.