Totally. I've even allocated investment capital for the sole purpose of putting a few Teslas into service as full time taxis on the Tesla Network.
I let people into my rental properties, why not other investment assets?
Because monthly rent is big, and leases are usually longer than a month. A Tesla Taxi is more like a motel room with hourly rates.
So, more like AirBNB than a leased rental agreement?
Different people have different boundaries and I respect that. I have no problem with renting my room/house out while I'm away, and I'd have no problem with renting my car out without me in it.
Prepare for your car to have interior cameras and a load of other sensors (e.g. smoke detector) constantly streaming to "the cloud." Of course, there will be no way to turn them off, because then passengers would do that. Then you just bill the passenger for the damages, and send him a link to the incriminating footage.
Then again, I would hate to use my personal car as a taxi, or my spare bedroom as a hotel, so I'm clearly not a good candidate for the "sharing" economy. Maybe I'm not desperate enough.
"and the ability to lock it's doors and drive someone to a police station"
That's unlikely, without a change in the law. Some modern cars do allow the doors to be locked remotely, but they don't prevent the doors from being unlocked from inside. Nor could I imagine an autonomous vehicle not stopping (for safety) when a door opened.I imagine that being able to identify the person renting the car, and cameras to show their actions, would be deterrence for most. For the rest, there's insurance.
Public infrastructure experiences a lot of vandalism and abuse. Prepare for your car to be treated like public infrastructure.