C'mon, the two are utterly incomparable.
SpaceX had essentially one body to convince - NASA. And given NASA's dependence on ULA to get things into space, and ULA's reliance on Russian rocket engines (aside from NASA's traditional conservatism and reluctance to support a brash new young Silicon Valley upstart company not doing things the NASA way) they quietly welcomed SpaceX with open arms, and paid SpaceX huge amounts for their development. Also, I'm not aware that ULA was a 'monopoly' in the usual sense of the word - they've not taken measures to suppress potential competition in the past, have they? (There's no launch provider badge system!). They were just the only US company that could offer orbital services at that time.
tl;dr, NASA had major incentives to support SpaceX, and ULA wasn't a true monopoly.
In contrast, Uber faced hundreds of different NASAs - each one the local government of any and every major city they wanted to enter. In each case, the challenge and the hurdles in their way would have been different. In each case, there were multiple long-established alternatives (the incumbent taxi firms). And in many cases, the lobbying power of the incumbent taxi firms on the local decision makers would have been considerable (via overt lobbying, relationships, threat of strikes, maybe even bribery). All of this would have made making the case for Uber in theory to unenlightened local politicians almost a non-starter. What worked for Uber was getting their service up and running (sometimes illegally), users seeing that it was a dramatically better option than the incumbent uninnovative taxi firms offered, and then leveraging that support, together with other forms of pressure, to be allowed to continue business.
tl;dr, local governments generally had disincentives to support Uber, and Uber faced multiple entrenched competitors, sometimes in a monopoly position.