Your idea is correct, except it requires enforcement.

All shorts currently are easily to identify with complete seller and brokerage information. More than that there is a red flag waved (FTD) if the shorts are naked. The SEC has investigated naked shorting many times and has never failed to find that it is a massive problem. But the criminal enablers (SEC) who should be enforcing the rules are part of the problem not the solution.

The SEC should be gutted and many should be in jail.