If you Uber to this location, can you hike and see the sights without a car to do the loop?

The loop is a road. If you Uber to a trailhead you'll have to Uber out and service is spotty at best. There's no shuttle.

There are trail heads before the main entrance but no service to be able to call an Uber to get out.

Not really.

Reservations required when I went

You can uber to the main entrance, but it's quite a walk to the trailheads and you still have a fee to pay as a pedestrian or as a bike rider.