now apply this problem of "potentially hateful depending on context" to more important stuff. some racists have abused studies on demographic differences to give hateful rhetoric some "scientific" backing, ignoring that you can't generalize from a population to an individual. this has led to mention of demographic differences being very sensitive subjects and sometimes labeled as "hateful". but i don't think we want to stop all research involved with this.

i do not trust the government to make these determinations about when context is hateful and not. since Americans are much less trusting of government than most europeans maybe you can see why we come down on a much higher bar for the government restricting speech and even higher for prior restraint.

let's take a counterexample from your country, where a man was sentenced to community service for a "grossly offensive tweet": the only good Brit soldier is a deed one, burn auld fella buuuuurn

he faced possible jail time. now i think this is more easy to identify as "hateful" than prior examples i've listed. i don't know if this was the person's intent, but in this case hate can serve a legitimate political purpose (anti-imperialism/anti-military industrial complex). similar to how "all cops are bastards" is "hateful" towards cops but again serves a legitimate political purpose (protesting police brutality, racial profiling, etc.)

so again, should anyone really trust a government to be the entity to determine what is "too hateful"?

Again, this is not an axis with good on one end and bad on the other. It's an axis between fewer limits and more limits.