This is why you most probably need to destroy the private keys of wallet A right after you signed the transactions.

This is terrible advice! Let's see what someone who knows a thing or two about Bitcoin said:
You should never delete a wallet.
This way, you only store private keys of wallet B (or simply use wallet B on a custodial exchange / wallet where you can login every time because you previously made the KYC) with 0 balance. With the custodial wallet, there is no risk of the exchange being hacked, because you don't store anything there, you will only use the wallet B if you'll ever need the backup. Best is to sign the same UTXO to more than one address and if you'll ever need the backup transaction just simply broadcast the one that you can surely access.
So instead of "be your own bank" and "not your keys, not your coins", you want people to completely rely on third party services and give them the power to broadcast away your coins whenever they want.