I don't think having "drivers spend as much of their shift as they can driving clients" is the best objective function. It seems like you should want to get customers to their destinations as quickly as possible, not have cars driving around slowly to maximize client drive time.
"You have to leave enough time in-between trips so the driver isn’t late for their next client." also seems bizarre, as you should just be routing the minimal time cost set of vehicles to those awaiting rides. This seems to imply most rides are scheduled pickups?
It's a perfectly fine objective if you trust your drivers to meet a minimum standard of a good job. It won't work in an adversarial system like Uber where drivers are just numbers but if the drivers are also invested in the success of the platform it's fine.
Given that drivers are driving the shorted distance/time route at the speed limit, treating customers with respect, arriving on time to scheduled pickups, etc. The next thing to focus on is scheduling/filling orders such that drive time is maximised.
"You have to leave enough time in-between trips so the driver isn’t late for their next client." also seems bizarre, as you should just be routing the minimal time cost set of vehicles to those awaiting rides. This seems to imply most rides are scheduled pickups?