Most people ( and a lot of people on HN) really believe that online platforms should be able to suppress such unlawful videos."Such unlawful videos." So basically, the government should be able to declare content "unlawful" and it's okay so long as public sentiment goes along with it?
Basically, you've simply thrown out Free Speech. I can understand why someone would find the video of the shooting shocking. Personally, I've chosen not to view it. However, if Free Speech isn't an absolute right, then it's simply broken.
Habeas corpus, the Presumption of Innocence, and due process -- what if the government could just suspend those things when it felt like it? Those human rights would simply be broken.
The difference between a just society and an unjust one, is that the just society extends the same rights and protections to all its citizens, no infringements, no exceptions. A society with Free Speech extends the right of speech and the right to read/hear that speech to everyone without infringement as well.
The interesting thing about the Weimar Republic, is that almost all of the laws covering human rights had an "out" for the government, allowing them to suspend the right, "for the common good" in emergency situations. As a result, the subsequent regime didn't have to change many laws to operate as a totalitarian regime.