"The knowledge" may very well at one point have been a reasonable requirement for a taxi driver, but at least as GPS satnavs got good, it's just not anymore. The purpose of "the knowledge" today is only to serve as a barrier to entry to protect incumbents against competition.
Edit: Footnote on doctors: It's a poor analogy as a taxi-driver taking a poor route (picking good routes is the singular advantage the knowledge provides) doesn't carry anywhere near as bad consequences for the "patient" as a doctor making a mistake.
It's kind of like if travel agents were regulated, and suddenly expedia or kayak existed. They can do an almost-as-good job through technology, and a "mistake" analogous to the taxi driver taking a poor route, i.e. Expedia connecting you through a worse city or not finding a deal 10% cheaper.
The same with self driving cars, its not like Uber or the taxi industry are long for this world without drastically changing business models (maybe 10 or 15 years tops).
It's sad but they are simply a victim of technology. Before sat nav, minicab drivers were very unreliable. They would get lost, they would have to consult maps, etc. Now, a minicab is as good or better than a taxi.
As usual it turns out that there are good & bad taxi drivers, and good & bad mini-cab drivers / companies too.
Part of being a good taxi-driver is knowing which parts of the city are going to busy at different points of time.
If a taxi takes a detour from the best map-presented route you don't know if they're giving you a faster journey, or ripping you off. Too often people assume the latter.
Google has all the information a cabbie has (road layout, major disruptions, historical traffic patterns, speed limits). They also have real-time traffic information. This is the kind of problem that computers tend to beat humans at, eventually.
Using the same kind of volunteers who contribute to OpenStreetMap it should be possible to update routing based on temporary road-works (which might last for 3-5 days, here in Scotland), which would otherwise catch drivers out by surprise with detours.
Assuming your conjectured startup somehow conferred the medical skills you would have just found a great way to lower everyone's medical bills.
Private car hire services (minicabs in the UK) does not have the same licensing requirements as black cabs (licensed taxis)
They'll still get hosed because without a medallion system bottlenecking the amount of suppliers, taxi service becomes a race to the bottom that can't support a decent living. But at least they won't be _twice_ hosed like they are now.
EDIT: I'm not saying Uber is wrong and should be stopped and the taxi drivers protected. On the contrary, the legislation could be opened up, dropping both protection and regulation of the taxi industry, now that Uber exists as a competing solution. However, the current state of affairs, where some drivers are taxed and regulated (taxis) and others are not (Uber drivers) is just going to make the former group collapse under the burden of regulation.
Also, I'm merely observing that opening the market to a huge supplier pool effectively means the end of the taxi driving profession (for reasons that have already been stated a hundred times before). Not saying this is good or bad, it's just the way the market works.
Cabs do not have a meter. The customer can set a price before the journey. These must be pre-booked by phone. In theory there is a lot of regulation around criminal checks etc.
Uber exists in a grey middle ground. They are booked via the app; and the app acts like a meter. The regulator for London has recently said that the app is not a meter and thus Uber is fine.
So long as Uber is complying with local laws I'm fine with them operating. I guess they should be prepared for some of the backlash they'll face when an Uber driver murders a passenger. (Because, with a large enough number of drivers and passwngers and years it'll happen some time).
I also suspect that the taxicab regulations would prohibit taxicabs from using alternative meters, so taxi drivers could not be Uber drivers at the same time.
[1] http://en.wikipedia.org/wiki/Taxicabs_of_the_United_Kingdom#...