Uber's main problem is that city governments are deeply connected with existing taxi structures - sometimes it's a matter of straight corruption, sometimes it's a matter of lobbying and existing relationships. But why can't Uber invest their money into convincing city governments into changing their regulations? Surely they have more cash to do so than individual taxi unions?
This is actually exactly what Uber does. The common Uber practice is for Uber to enter a city under circumstances that range from legal, to questionable, to clearly illegal. They will then rush in with lots of marketing and lobbying to sway both the general population and the local government and earn a foothold in the city. Once they have secured this they will push for local legislation if it is required. In generally they are very successful in practice as they operate in over 570 cities and are a multi-billion dollar company.
For example in 2011 Uber received a cease and desist letter from its home town of San Francisco. However Uber remains legal to this day. This was in due to in large part its foothold in the populace, the work of its lobbyists and direct negotiations with the government.
Obviously though that doesn't always work. The most famous case of failure here would be Prop 1 in Austin, Texas. Both Uber and Lyft spent over $5 million trying to legalize their practice there. Ultimately though they were rejected by voters and left the city.
The question seems to assume that the only reason for business licensing and regulation by local governments is because of monopolistic cronyism.
Many of the licensing requirements for taxi companies is for the benefit of the local citizens (many require that they act certain ways in procuring business at airports, that they offer services to certain areas, that they offer services specifically for the disabled, etc). These requirements to do business in those regulated categories incur costs to the companies being regulated. The cities also generate revenue from the licensing (another cost to the companies).
So, the established businesses have incurred significant costs and met regulatory standards, often for decades, and that is often a reason why they are not in favor a competitor coming in who does not have to meet those same expensive requirements that they did/do in order to compete in that marketplace.
It's not that the companies lobby to lock Uber out (might not be against it, per se), though that might be the net effect. They lobby to demand that the same standards that are imposed upon them be imposed on the new competitor.
But why can't Uber invest their money into convincing city governments into changing their regulations? Surely they have more cash to do so than individual taxi unions?
Maybe. But do they have more voters? Not only do taxi drivers have an incentive to vote against Uber, but other unions may join them. And unions are also a source of volunteers for political campaigns. Union influence in government is larger than most statistics can measure. In many places, being the clear anti-union candidate is a clear loss.
And it's not clear that they have more money. Taxi medallions cost a million dollars in New York City as recently as 2014. There are more than thirteen thousand medallions there alone. That's roughly as much as Uber has raised nationally.
Another issue is that taxi operators are local. So all their money is spent locally. Uber has to spread its lobbying out over multiple countries much less multiple cities.
But why can't Uber invest their money into convincing city governments into changing their regulations?
Because fundamentally Uber is in competition with the local government. The existing taxi system is a valuable revenue source for the governments, for doing practically nothing.
Uber fundamentally replaces or bypasses the government and connect service providers to customers.
When you take the governments candy away, they aren't going to be happy.