It has been explained so often to you, but you do not want to comprehend: In Berlin you got what you would call a limo in the US or a minicab in the UK. Or as you wrote "but a typical car and driver like one would find in the USA howbeit better cleaner Mercedes and a courteous driver.". Our system calls these services "Mietwagen". They are not generally regulated. They offer fixed fares or alternative arrangements, in Berlin probably the double of what you would have paid for a taxi.