I agree that simply emailing in copies of identity documents after the fact shouldn't be sufficient. However, there should be a verification process that includes verification of identity documents through legal means, including perhaps a processing fee. The fee would preclude many attackers from even trying to break this process.
Maybe this would only work for new accounts as you'd probably need to provide identity information on before losing access.
Maybe this would only work for new accounts as you'd probably need to provide identity information on before losing access.