It worked some places for decades. I think crowded urban areas have every right to tightly regulate limo services. However out in the burbs it's another story. The only way to avoid drunk driving in the burbs for many years was to not drink, and that's a bridge too far for a lot of people. I have no idea if there are stats, but anecdotally, I can say that Uber/Lyft have stopped me from getting behind the wheel after drinking many times. In the old days, you'd have to call a cab, wait an hour, then hope someone else didn't just hop into your ride, because the cabby didn't give a fuck who he was picking up. The thing about Uber is that there's plenty of room for them to make money in a regulated environment. If they were smart, they'd work with the government to try to shape regs, rather than oppose any and all attempts at regulation.
You're not arguing for deregulation in urban areas, you're arguing for less-stupid taxi regulation. I agree - taxis were and are awful. They were an industry ripe for disruption. But that disruption should be along the lines of "this medallion allows you to dwell in this zone for this many hours a day not including 4-6pm and therefore costs 10% what a full one costs."
I'm arguing for safety realized through convenience. That could be satisfied by taxis or by competing services. The thing I know is that there is no way before a couple years ago that I could get a car on demand within 10 minutes at 1:00 am on a Tuesday. Uber's regulatory conundrum notwithstanding, I would like to continue to be able to get that car when I need it.
Taxis are regulated. "competing services" are not. I will happily agree that the companies that operated within that regulatory framework were ossified and anticompetitive but that's an operational problem, not a structural one. Your 10 minute 1am car is earning its driver $3.50 an hour and costing its company five billion a year. Yes, it's convenient but it also isn't steady - state. The argument here is that venture capitalists are underwriting a Dickensian lifestyle for the drivers and fucking up traffic for everyone else and should Uber's note holders decide they're sick of the experiment, we'll all be paying market rates once more.