Taxi companies do have apps "free now" (formerly "mytaxi") and "taxi.eu" that majority of them use. The functionality is more or less the same as with uber.
I'd be happy with FreeNow instead of Uber, if it was available outside of large cities. Many taxi drivers still refuse to sign up for FreeNow. I spoke to one taxi driver and asked her why she wouldn't use FreeNow and she mentioned something about the fees being too high. Of course, she only accepted cash, too. I was just glad that I wasn't getting yelled at for paying with a 50 Euro note.
There are still a few people that use it exclusively, but they're getting rarer each year. You can pay with cash almost everywhere though, so I can understand how this believe keeps getting repeated