The difficulty is that there's still no guarantee that an Uber would be available. It'd just take care of the request part. Would need to be some thinking around what if there's none available in the area etc.
Would it be possible to create something that effectively books an Uber for a later time/date?
An example would be I know I'll need an Uber tomorrow morning at 7AM so rather than get out my phone at 6:50AM I do it the night before and it just delays the request until the morning? Perhaps even add in some push notifications or something to check that you still want to book it and all you have to do is hit yes/no.
I chucked mine up there and will be keen to see the feedback. Also thought the way it just keeps loading is fantastic. Easy to get on a roll as @prawn mentioned.