Taxi licencees in most large German towns/cities have to accept credit cards. If you use mytaxi /freewhatever you pay with the app. Uber in Germany is just a middleman brokering limo services.

Some taxi franchises (like Isar Taxi in Munich) require the cars to be of a certain standard (clean <5 years old etc). Also in Germany you can take any taxi in the queue. If you see a banged up dirty taxi in the stand you are free to take the one that appeals to you in the queue.