This is a good solution to your problem, however UX is also used to achieve business goals. Uber are very savvy and I believe they have motives behind discouraging price comparisons.

The original concept behind Uber, before they were all about disrupting things and the sharing economy was to provide a service that would allow everyone to feel and behave as if they had a personal driver.

Part of having a personal driver, is that money doesn’t matter— you summon your driver and they take you somewhere. I think they have tried to encourage this behaviour so that people don’t focus on the cost and just focus on the benifit.