Doing this for a class project and need to write up a comprehensive case study. All problems I can think of have solutions that have been already announced or launched.
I wish they had a pickup-my-friend feature. When my friends are drunk I end up calling Ubers or Lyfts for them, on my account. But the problem is: I can only do that for one friend at a time (because Uber thinks I'm in the car that just picked up friend #1). I wish they would let me specify who needs to be picked up, and give some basic stats like Name, Phone #, etc... and I wish they would let me do that for multiple people in parallel, and let the rides happen concurrently.
A panic button. Would allow a passenger to alert Uber / Police in the area and transmit location and info immediately to prevent things like rape, kidnapping, etc.