Bottom line the extra license for the driver is cheap, perhaps up to 1000Euros, and as it is not a real cab, they don't need the cab permit from the city (AFAIK).
Uber's and Lyft's business model relies on individuals driving their own cars, many of whom do it part time to make a little extra money. A thousand euros is a very significant hurdle to someone like that. Maybe cab drivers should be required to obtain a special, more expensive license, but it's not convincing that this license is no big deal because it costs "only" 1000 euros. I'll take your word for it that Berlin doesn't require any extra permits, but FYI cities in the US usually require cab companies to obtain a so-called "medallion" for each taxi they wish to operate. There are a fixed number of medallions, which limits the total number of taxis. In NYC, when a medallion becomes available, it can go for upwards of a million dollars. In other large cities, the cost can be in the hundreds of thousands of dollars. It's clear why both city governments and established taxi companies are fighting tooth and nail to get Uber and Lyft kicked out of their cities.
Why? Because I don't want to bleed to death when a friend flags down a 'cab' and asks to get me to the next hospital and the stupid driver takes the third best route to the second closest hospital or needs 3 minutes to pick one from his navi.
Ridiculous. Regardless of whether an Uber driver is qualified to drive a taxi, a taxi is not an ambulance.
The EU has a lot of consumer protection laws designed to look after their residents (now there's a thought), a concept that is completely foreign in the US where it seems that only company profits matter.
I'm sure all of these laws exist only and exactly to protect residents rather than established companies, trade unions, professional organizations, and other political donors against upstarts like Uber.
If you can't understand it, it is intuitively obvious.