You don't seem to be understanding. The regulations themselves don't stop innovation directly, but the fact that it's very difficult and expensive to get a medallion, plus the fact that once you cross that barrier, you'll be protected by law from much new competition, means that it's harder for new players to enter the market and compete.
The medallion system is stupid and should be done away with. It's purely anti-competitive.
Again, you're right on the fact, but not on the interpretation. The medallion system used by most cities restricts the number of cars on the road in a city. However:
1) Most taxi fleets -- especially the larger ones -- collect monthly rent from car owners, rather than own a ton of medallions themselves. The medallion system benefits owners of medallions, not fleets. This distinction, while invisible to the masses, is incredibly important.
2) It's definitely not rare for new fleets to pop up. We talk with plenty of folks who own fleets that are only one or two years old. All you need is a subset of drivers (and/or owners!), a couple of regular clients, and a little gumption. New fleets are popping up, and trying to innovate as best they can. The new, lower-priced, often mobile-based dispatch systems I mentioned in a previous comment have really been a boon to this segment.
3) In most cities, black car licenses are similarly restricted to medallions. The limits may not be posted, but they exist. In fact, a great article about Uber in The Atlantic exposed this issue in DC back in May[1].
4) Again, fleets working with us are achieving similar results; companies like Hailo and GetTaxi (who seem to be trying to work within the system) are as well.
In short: the medallion system is a red herring when it comes to stifling innovation. It is definitely an issue, one that tends to marginalize drivers and unnecessarily restrict supply for passengers. But every one of the companies you and I have mentioned abide by the restrictions it imposes, so your point is moot.
Going back to my original issue: I have no problem with challenging rules, conventions, and decisions (I'm an entrepreneur, posting on HN... do you really expect me to disagree here?). My issue lies in Uber's underhanded approach, where they both flout actually sensible laws and arguably force governments to send C&Ds by refusing to engage with them when initially approached.
The medallion system is stupid and should be done away with. It's purely anti-competitive.