I think technically, it is implementable. That is, bitcoin owner can state somewhere in the block chain that bitcoins in that address cannot be sent, which can add one more level of security. Also, the owner can voluntarily reveal his identity in public, or to a trusted third party.
Anonymity should be an added feature, not a mandatory feature, and that will improve the overall security.
1. Anyone can state "this public address is me" right now. You can be non-anonymous without any feature changes.
2. A private key states that coins cannot be sent. That is its function. No additional feature is required there either. If you require a second or third signature for more security, then use multi-sig for the trusted third party.