First it would make it extremely easy to scam account buyers who do not think to ask for a signed message and would make any buyer vulnerable to having their account taken back in the event they lose such signed message. It overwhelmingly appears that the OP is almost certainly trying to scam the person that he sold his account to. The OP proved his account ownership by signing a message contained in an other person's post (but not his own) so anyone buying his account would likely not be able to easily find such address to request such signed message.
You're chalking up account buyers as morons that don't know what they're doing. If someone's buying a BCT account, they're likely not a newbie to the community. Even if they did not think to ask for such proof, that can easily be solved with a public service announcement. If the buyer still chooses to go forward with the account purchase without some kind of signed message as a receipt, then it is their risk to take.
You need to remember that the person who is in control of the account at one point somehow controlled the password so the burden should be on the person claiming ownership not on the person who controls the account presently.
And what kind of proof would the OP have to present to satisfy that burden? What would it look like? What form would it take?
... if the administrators were to be as liberal with account recoveries as you are suggesting then theymos would be overwhelmed with requests for account recoveries and this would take his time away for more important work.
Of course, that is just your hypothesis. My guess is that with a more clearly well-defined recovery procedure it would allow theymos to restore more accounts back to their legitimate owners. Of course there's no way to know for sure without trying. And why favor account buyers at all? Theymos himself said he doesn't condone the activity anyway so worrying about account buyers getting scammed is a moot point.
Couple this with email confirmation on changes to vital account detail, like you read from my other post, that will cull out the majority of the account request to start with.