In Copenhagen Uber made a splash until they decided they didn't get all they wanted when the taxi legislation was liberalised and they left. My reading of it is that they didn't want to give other European countries ideas and they were losing money anyways, so it wasn't really worth it to subject themselves to the same kind of regulation that exists in London or New York.
And what did we get instead? 5-10 different taxi apps offering taxis at much the same speed it takes to get an Uber, but regulated locally and paying taxes. It's literally a question of installing a different (or multiple different) app and then the flow is the same.
The kicker: Uber came to Denmark late enough that the taxi companies already had apps (or at least some of them which was then the ones I used). Ultimately it was just a big fight over nothing and Uber left with red numbers and a bad image.