And Uber solved that problem. For it's local market. The thing is - why would it have to 'disrupt' markets that don't really need disruption or solve problems in markets where those don't really exist? Yet with it's enormous funding and hence market power it can take over markets around the globe, where the dude trying to make a living with his 5-cab taxi company or the student driving his one cab on his own can never even remotely compete.
Cab switch over hour sucks, but I've also been in a busy parts of Manhattan with plenty of Uber cars showing on the app yet can't get an Uber car to my location.
I've also noticed a drastic decline in the state of UberX vehicles in the past few months (I assumer from their aggressive recruiting effort). Used to be every UberX that picked me up was very clean and typically nicer cars (occasionally getting picked up by Range Rovers or Town Cars). Now quite a few of the cars are messier/dirtier than any cab I've ever been in.
I'll continue to use Uber and UberX when convenient, but I've cut back quite a bit because the drop in quality.
Now a system that combines the desired properties of the old system with better efficiency is certainly thinkable and desirable, but Uber is not that system, at least not in it's current incarnation.
How would you feel if your taxi driver told you: "oh sorry Sir - you want to drive home? Today that'll be 5 times as much as usual. We are kinda busy, ya know". Unthinkable for taxis. Accepting for the 'disruptor'. All but very rich people would rather wait a few minutes longer to get a taxi than to pay up to 5x as much as usual.
I'm happy if all the Taxi companies die because they aren't providing good service. Uber and clones let you tap a couple times on an app, know instantly without asking anyone if there are cars in the area because you see them on the map, and then watch the cab come to you on the map. If the driver has trouble finding you they call you. Then at the end payment is all automatic, you just get out.