I believe the main reason Uber and AirBnB both grew extremely fast is that they adopted a new (is it really though ?) approach to startups: fake legality until you make it legal.
The idea is to pick an illegal activity in a somewhat grey area and to start making money without bothering about legal until you're big enough to lobby your way out of it, either by way of "job creation", PR or just money.
The main reason most people did not try to build Uber or AirBnB before is because they stopped at the analysis step with the conclusion that it would be illegal, against regulations and thus an unwinnable battle.
Uber delivers an awesome affordable service by a) offering a taxi service, b) circumventing all taxi laws, regulations, ecosystem and related costs and c) enabling their drivers to not declare their revenue.
By cutting a few middle men, spending $0 on regulatory compliance and having a few "a little money on the side" drivers, you end up with better prices, happier drivers and none of the sluggishness of bureaucratic processes that prevents simple reviews from ruining a driver's career instantly.
At this point in time, a lot of the services offered through Uber are at least partially illegal.
Answered 6 years ago