It doesn't seem that car2go-style cars get vandalized a lot; next-user reporting controls most of what goes above a level of vandalism (smoking users and some trash in the car is normally not reported).
Rage against uber by taxis has been more rampant (imho); so if we add bus drivers, lorry drivers, taxi and Uber drivers, etc. there might be a lot of damages on the short term. But once these displaced workers find another job that vandalism will disappear, so it will be transient during adoption times only.
I notice the Car2Go (or e.g. Zipcar) next-user reporting system depends on their knowing the identity of each user at every point in time. Which is presumably also true if you've used an app to hail or summon an autonomous vehicle... Still I guess I was nostalgically imagining something like the relative anonymity of today's cash-fare bus services. (Though even those are loaded up with surveillance cameras.)
I guess it's too much to expect Americans to act like the Japanese when it comes to taking care of public spaces.