It's definitely an interesting idea. Though one of the major features that I love about Uber/Lyft is that I don't have to worry about paying in cash.
I know what you mean, but the Bitcoin integration is going to be really exciting!!!
For example, if I was paid the equivalent of a 50 USD ride in Bitcoin in Jan 4, and were to go to buy food today, I could only buy 40 dollars worth of food.
Which currency does that? Sure there may be a few examples in case of extreme inflation, etc, but it's not the norm at all.
I won't be paying any bills with Bitcoin any time soon.
Anyway, both a cool idea and a challenging one. Best wishes!