The only problem here is that this would limit the usefulness of the service. The most likely end game for this feature is that most downtown areas have a bunch of drivers fenced in, and nobody can find a ride to or from those areas. There are a ton of people in suburbs that would like to not drive into or out of the downtown in my area, and we use services like Uber/Lyft to avoid this. If the drivers in our area confined themselves to just near the downtown, we would have to drive there either way, and so the service becomes useless to us.

If the service instead allowed drivers to designate a "home zone" where the base price is payed, and then trips to successive neighboring zones have a multiplier applied, this would probably work better.