@alonmuroch thank you for suggestion!
First of all, this is close to the scheme we are currently using in the TokenBridge: validators collecting their signatures in the sister chain and anyone then can send them to the main chain.
Next and this is what meets lots of criticism, that such scheme relies on the trust that validators will always be able to perform the signature. So, the user’s need to withdraw tokens depends on the validator’s ability to sign the withdrawal request. If they don’t sign, the user will not get funds. The proposal we described above get rid of this limitation: a honest user don’t need to collect the validators approval, so, he/she will always have a chance to withdraw funds but with some delay – a low price for the huge benefit.