I think that if Bitcoin allowed users to insert some identification such as their name or an email into the users transactions then if an attacker stole money from the user it would make it a lot easier to report the theft such as if the attacker tried to change the currency into dollars by exchanging it with a bitcoin trader...
No need to embed the identification in the transactions, I don't think. You just need to associate your public keys with 'you' at some place where anybody can see that association and prove that you originally owned the private keys associated with those public keys.
Let's see, I think something like this would work:
For every private key in your wallet:
Grab the corresponding public key
Sign it with the private key
Compute SHA256(public key, signature, "your name and email address")
Then upload all of those SHA256 hashes to some secure central database somewhere, which stores it along with the time it was uploaded.
Now if somebody copies your wallet and spends your coins, you can prove that you had the public/private keys in the past by showing everybody the (public key, signature, "your name and email address") that hashes to the value in the central database.
The crook can upload their own SHA256, of course-- this relies on you uploading before the crook.