A quick thought: do taxis actually work? After being in some danger of missing a flight after a cab failed to show up and a new one had to be procured at short notice, I thought back on all the hours (probably three or four hours in total) I have spent pacing up and down awaiting a taxi to arrive. It's got to the point where, if I have to book a cab (and I realize that I do this quite rarely, probably because I hate the waiting so much), I have to book it sufficiently long in advance that if it doesn't show up I can ring up and call for another. Which seems to rather defeat the point, now that I think about it.
I don't like taking taxis as a matter of course. If there's a way to do it on public transport then I prefer that, even if it adds up to an hour to the journey (which is probably what you need to allocate to allow for the cab not turning up). But if you have to be at a station or airport early in the morning, or you have a lot of heavy luggage, then a taxi seems to be more necessary.
If you can go somewhere that there are always taxis hanging around, like, er, out the front of an airport, or, er, New York, then it's OK. But even at most railway stations, there always seem to be taxis out front, except when you arrive at one and want to hail one.
I think the source of my anxiety and irritation is that it's a very one-sided game. If the taxi you ordered never shows up, then there's not much you can do. They probably have enough business that theloss of your fare is no great loss. And because ordering a cab is such an impersonal business, you never really know who let you down, so it's not like they lose your custom.
I think the only solution is to institute some private system by which individual members of the public can own and operate their own automobile vehicles. It will be dreadfully inefficient, there will be all kinds of probelems from inexperienced operators, the problem of where to store all these additional vehicles and so on, but given the problems with using taxis, I think it must be the only option.