They would be the physical equivalent of open source software which also "belongs" to no one.
Nope. A software is immaterial. It cost nothing to copy. It's different in robotics, unless you build a self-reproductive robot. Wild science fiction again.
The more BTC stored inside the robot, the smaller the chance of vandalism.
Destroying a "wealthy" robot for fun would be the equivalent of you finding a safe on the street that you know has $100,000 inside it, and then dumping that safe in the ocean, just for fun.
If someone has really no hope in hopening the safe, they would throw it for sure.
Plus, throwing a safe is certainly less fun than destroying a robot.