So, what's next?

Taxis are user-unfriendly. You have the communication barrier with the taxi driver. Their means of getting paid are highly erratic ("The payment machine is borken, cash only"). The driver is unregulated and the level of service they provide may be problematic (I once had a taxi driver unpromptedly start listing the advantages of the historical Nazi Party while riding in Leipzig, and a taxi driver who took me on the Moscow grand tour for what ought have been a four mile trip...). And when you order one, god only knows when it will arrive.

Uber worked for customers in part because they had a unified interface to call - and see the availability - of taxi services that worked in several cities and countries, and because it took away the payment barrier (credit card always works). And you could have a look at the map and see when you would need to get out of the building into the pouring rain to catch the ride.

Some countries have since created similar schemes for traditional taxis, but those often are city and/or country-specific. Works for the urbanite who stays in Berlin, but woe upon the traveller.