I’ve pondered this question of choice myself while waiting for an Uber to arrive; though my perspective was how useful it would be to be able to choose from the available vehicle types being driven in the vicinity — from the perspective of the Uber X model — as this would save the awkward attempts to load luggage/furniture/a lawnmower into a too-small vehicle without damaging it.
Having said that, the downside to this level of choice is that it might unnecessarily create a “penalty box” situation for drivers who were ranked below 5 stars. If customers consistently choose higher-rated drivers, this prevents the non-5 star from repairing their score.
Don’t get me wrong, I understand the importance of passenger safety within the Uber model. One of the reasons it’s preferable to regular taxis is that it’s upfront with ID’ing the driver and showing their customer satisfaction rating. However, I understand that Uber is quick to discipline drivers of whom complaints are made (for example by withdrawing their access to the app), so the risk here is that — for example — a relatively new driver whose rating was knocked down by a passenger having a bad day (assuming that the rating is proportionate to the number of rides) might be unfairly penalised.
I do agree with your suggestion that the app display the number of hours the driver has been on-shift, as this is an important indicator of fatigue. I’d also suggest that perhaps the app should offer a preferred driver gender option, as having a female driver might make female passengers traveling alone feel more comfortable in taking an Uber.