So the argument is that if they just froze trades (both buying and selling), then people who own many GME shares and want to sell would not be able to and there would be a subsequent backlash? Maybe? I am trying to compare the lesser of two evils here and it still seems like they made a poor choice.
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.