>I wonder why her trade-off is morally superior?

I mean, if you start using your thinking cap for a few minutes it makes sense.

1. The number of drivers is small. The number of passengers is large. This makes checks on drivers technically possible.

2. Drivers work in their own cars. Are you saying they should get bars installed between the back and front of the car?

3. The passengers are the random public, do you want to submit a criminal background check before riding in a car?

4. These are all things Uber can do themselves to protect their employees. These are not things the public can do to protect themselves from Uber employees.