A lot of the time, private keys will get stolen contemptuously with an account getting hacked so this wont necessarily solve anything.
Also, the administration will look at a lot more than the signed message when considering to recover an account.
Such as what?
If someone delivers couple of signed messages with a couple of BTC addresses posted here, what other proof could you need? If that doesn't cut it then nothing would.
Like I said, most people getting their accounts stolen is due their emails getting hacked. Getting your private keys stolen is much harder if you are keeping them safe.