That is not how Bitcoin works.
When you ...
By the same logic you could steel my car and claim that I gave up any rights to it when I bought it. Bitcoin IS my property and the government (at least in the US) has an obligation to assist me if I was robbed. They took their taxes when they claimed it was mine, now they must act. Which is why they can tax me in the first place. So while the police may not know what a bitcoin is, I have protection for my assets.
No, you don't understand what I am saying.
Your example does not work since a car (and other types of major property) has title ownership papers.
Bitcoin has no such proofs and that is intentional in this system. Your only proof is control of keys.
The US Government has no obligation in law in help get your btc back UNLESS it was secured,
such as with exchanges or businesses. As long as you deal with bitcoin within the Bitcoin Network,
there is no remedy. When you move your btc to something else, like Coinbase, then that is the only
time the US government would have ability by law and proceed with their investigation/processes.
Here are some questions:
1. If someone swept my btc from my address outside a regulated system, what is the mechanism and
protocols to legally and realistically help me get my btc back?
2. What are the proofs that are used to prove that I didn't transfer the btc myself and made a false claim?
I checked with my insurer (I insure my coins) and he tells me that id stolen my BTC are absolutely something the police are legally obligated to investigate and that the thief is open to both civil and criminal prosecution.
However you are asking the right questions about how practical it is to recover lost bitcoin. I have no idea how they would determine who the thief is in the absence of other clues, or how you could logically prove that you were robbed. Then again, this is true for a lawnmower also. I suppose the police would try their best in an investigation. My hunch is that they would be unsuccessful. That's why I prefer insurance.