No, that's not the idea. If surge pricing was in effect all the time --- if travel pricing was always an auction and drivers were kept scarce to keep prices up --- then Uber rides would be a service for the rich. But disasters are rare, and the surge multiple is merely the equivalent of several Uber rides instead of one. Meanwhile, the alternative to surge pricing is a high likelihood of not getting a ride at all, because disasters suppress demand. It's hard to see the class-warrior logic in this situation.
(Later, you edited your comment)
It's a caricature to suggest that "Coase" is, to economists, a license to apply the free market to every public policy problem.
Meanwhile: you have to actually make the case that there's a distributional problem with surge pricing for Uber rides. If the alternative is no rides at all, then surge pricing makes some people --- not all of them rich --- better off while making nobody worse off.