Exactly, stopping buying prevents people from (potentially) making money by buying the stock low, whereas stopping selling (potentially) prevents people from losing money on the stock they already own, from the platform which they bought it.

I can't imagine the backlash if the completely froze the stocks while the market kept going.

But preventing buys on the broker with the most trades of these stocks directly leads to a price drop; this leads to loss for every current holder of the stock.