I've been thinking about how to deal with this a long time. I expect one day the government will have departments that monitor addresses associated with "lost" keys which, if moved, will trigger a violation of some kind of court order triggering an order to show cause for the person to show up in court and justify the moved money.

I should add, we're fortunate (sometimes) that the rule of law we have in the US doesn't require definitive proof in the cryptographic sense but can be established through credible testimony. Sometimes it's not a good thing, but I prefer this aspect of the law as is.