Naked shorts let you create stock out of nothing, which you can sell to drive prices down (and ultimately make money off of, since you can rebuy more cheaply).
If you can’t do that then you at least have to get the cooperation of someone who does own the stock in sufficient quantities - and their interests are probably against yours since they, y’know, own the stock.
Banning recursive shorting would be a nightmarish enterprise, since each individual share would need to be tracked to see if it was already shorted. Banning naked shorts supposedly does enough to discourage the behavior. We may be seeing that to not be the case.