As far as I know, anyone can write a wallet. All a wallet is is an interface to the blockchain ledger. IMO, registering wallets won't work for them. People would write their own. Wallets on exchanges and coinbase, yeah, they could register those, but people who didn't want to be registered would simply stop using those services. Decentralized exchanges are being created as we speak. We could use those. Not to mention people who get their coins from mining. No way to register the transfer from the network to your account.