Robots belong to people. There is no point building a robot who belongs to no-one.
They would be the physical equivalent of open source software which also "belongs" to no one.
I also disagree about vandalism being discouraged. If I had such a robot in front of me, I could destroy it, not for the bitcoins, but just for fun.
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.