But if you don't make the order and everyone knows the reason is that the cops might not listen to you, isn't that having the exact same effect of making you look weak?

Now, Mamdani isn't this guy, the fact that he didn't purge Jessica Tisch on his way in proves as much, but the way a mayor is supposed to impose discipline on the cops is by firing ones who don't listen to them and replacing the leadership with loyalists.