Is there a way that MtCox or somewhere could keep a blacklist of 'stolen' coins? So that they become worthless because nobody would be able to trade them?
but it'd be viral so be universal. Merchents and absolutely everyone would all quickly start checking just to ensure they don't get coins they can't trade, making it effectively universal.
Which means it comes down to convincing the gatekeeper that you were burgled. But that's a human level problem.
and whoever that controlled that list would basically control bitcoins, because they could charge a levy or else they'd put your bitcoin into that list.
I've seen this suggestion pop up many times in all sorts of discussions on bitcointalk.org forums. There's a bunch of pretty good reasons not to do it, I encourage you to look up those old discussions yourself.
"Decentralised crime fighting using private set intersection protocols" - Mike Hearn
https://bitcointalk.org/index.php?topic=157130.0