The question is: What's ownership? How do I ascertain that I own a device and not, say, the guy who just robbed it from me at knifepoint?

From a government perspective, I think the issue is anonymity. In the long run, governments cannot accept ownership of a thing without being able to attribute usage of that thing. From that perspective, as much as you cannot anonymously own a warehouse, you cannot anonymously own a programmable radio device.

From the corporate perspective, it's even worse: They cannot accept you using a device freely if they license you software or data. They would probably be fine if you could prove to them that you were not violating the terms (or vice versa, they could prove when you did), but that probably has a massive impact on privacy.