Uber uses Braintree for payment processing[1]. Braintree already has integration with Coinbase[2]. I assume that bitcoin transfers being push (instead of pull like credit cards) is the reason they haven't activated it.
Uber already has "uber credit" system, for example promotions where you get $10 in your uber account. They could very trivially just add option, where you could add uber credit to your account with bitcoin (or any other push-only payment method, for example cash via coupons).
Yeah but that goes against their "press a button for a taxi" philosophy.
Correct me if I'm wrong but I believe you can make pulls from coinable wallets provided you have enough money in there.