for example: if you get a private key which creates a given address, you may mark it as "taken"
...and when you'll want to recover an address from its private key, you won't be able because it's already taken; the blockchain won't know it was you.
Such a setup can work only in a system where it will be needed to identify
you as owner.
It does not need to be so strict, it even does not need to be able to identify the owner. Just a mark that there is someone who is able to sign a message for that address.
But I do not see now any practical use for that.