A key is just a 256 bit number. You can literally create one with paper and dice rolls. They will no sooner figure out who is holding most of these than they will figure out who is holding cash, or the identities of the 25m+ people downloading pirated media right now.
At best they can ask the public to please turn over their private keys, which will go about as well as efforts to stop piracy.
They can prosecute transactions with unregistered keys as money laundering. They may not have the resources to get everybody but they can collect a few scalps pour encourager les autres.
Yep, they can also prosecute merchants who accept payments that don't go through "approved" middlemen (banks, etc), or even ban/regulate crypto that allows users to make their own keys.
At one point the US gov was building their own crypto currency, and I'm sure it wasn't because they felt the existing options weren't private enough from oversight.
> key is just a 256 bit number. You can literally create one with paper and dice rolls
Well sure, but if you want to actually use it you need the whole keypair. Unless you're really good with you elliptic curve abacus you're going to need a computer for that l.
At best they can ask the public to please turn over their private keys, which will go about as well as efforts to stop piracy.