an industry that has been competitively fragmented and structurally stable
Rather than "competitively fragmented", I think "local monopolies" is the proper term. E.g The service offered by London black cabs is horrendous. If there had been any proper competition, they'd have gone out of business long ago.
No one can demonstrate a clear link between specific Uber product features and its meteoric growth
They have an app which allows you to order a ride in most of the Western world, and they accept credit card payments. I believe just those two advantages over most incumbents are enough to explain their popularity.
explain why no one else had ever recognized these opportunities
Because the incumbents were so entrenched that they could afford to sit on their asses, considering the multiple layers of regulation protecting them, and it was so hard for new entrants to get into the market that it took near-organized crime methods to do it.
or document how they are powerful enough to allow Uber to rapidly drive all incumbent taxi and limo companies out of business.
As soon as any alternative to the incumbents was created, customers couldn't switch fast enough.
Uber has broken the laws in many ways, but I for one am really happy that the incumbents got the kick they deserved. And I'm not really worried about Uber becoming a global monopoly, because it's actually easy to replicate the business model. You just need not to suck.