It already happens with shared bicycles, shared electrical 2 wheeled scooters and other stuff. I don't see why it would be different from this ones to suffer from vandalism and plain stealing/damage.
It probably won't. There are loads of those bicycles and scooters in Seattle, most of them are tagged with graffiti, I often see them dumped down stairwells and scattered in alleys. Those don't carry any interesting cargo so they're really only a target of mindless vandals, if they had fresh pizzas in them they'd get attention from a different group.
Pneumatic tube systems have been around for ages - but I can't see them scaling up too well. As for drone systems - well, they will have a number of issues in city environments.
Wikipedia has a reasonably good article covering the 19thCentury Paris Pneumatic tube mail system, probably one of the best known.
https://en.wikipedia.org/wiki/Paris_pneumatic_postThe real problem is people taking old technology and presenting it as a 'new untried thing'.
I remember those pneumatic tube systems at bank drive throughs when I was a kid, I always thought they were cool. I've seen them in retail stores too although I don't recall where or when the last time I saw one was. When you need to transport small physical items around over a modest distance they are a pretty good solution I think. It's only the need to do that going away I think that has reduced their use.
Why would a solution need to work everywhere? It makes no sense.
Because the companies behind this are pegging their success on growth and that everyone (or a huge percentage of cities) will want this. They don't want a small niche market, and many may not be able to survive within one.
But ok, let's assume that a company stays small and niche and continues to supply a niche market forever, great. But that means our lives haven't all been changed by these delivery robots like all the articles like to extoll.
There is always marketing hype. As I wrote before: big, densely populated cities have lots of delivery people driving around nowadays so there is an incentive to reduce costs. The thing is that in a densely populated city you don't need to cover a large area in order to service a large amount of people. Due to high house prices you'll find people there that have money to spend on extra services as well. Drone delivery isn't for suburbs but for city centers.