The real reason they won't replace him is that he built a unicorn from nothing for them, making them very rich and cool in the process (imagine being able to say "I was an early stage investor in Uber"), and by all accounts he has not changed, with Uber being run as a large, efficient company that delivers globally with McDonald's level reliability.
Investors also know that what people say and do are very different things. In aggregate, customers will publicly complain and say they will take Lyft, but privately will vote with their wallet (after all who sees what you book), in the same way that publicly they decry energy wastage whilst they take holidays on other continents and drive SUVs to their giant McMansion. I literally cannot think of a company that "won" by promoting its ethical competitiveness, beyond conquering the few percent of the market who can afford to care and care enough to pay a premium. I wonder how many of the #DeleteUber reinstalled it quietly a few weeks later. The public has a very short memory - as a Frenchman I remember being called cheese-eating surrender monkey by the same Brits who today protest against "American imperialism".
Governments won't do anything since Uber has tons of positive externalities such as reduction in drunk driving, creation of many part time unskilled jobs and generally electorate happiness in having a reliable and affordable taxi service. They think in terms of net welfare and a few Californians having some issues at work is the least of their worries.