I like this feature request; I think it will enable even more interesting uses of bitcoin. I created a feature request at github for it.
Example: a store that accepts bitcoins could verify that a customer sending in a question about some transaction actually IS the same person who sent them the bitcoins, by asking the customer to sign their message using one of the same bitcoin addresses they used to sign the coins.
If the "store" is a privacy-focused VPS provider and the question is "Hey, I lost the root password to the virtual server, could you generate a new one and encrypt it with this gpg public key", then tying that message to a bitcoin transactions is extremely useful.