Is "I think black people should be enslaved" fighting words? What about "All jews should be gassed"? Where do torch-wielding mobs marching down the street fit into all this?
See trope 7 from Ken White, a noted lawyer and first amendment expert - https://www.popehat.com/2015/05/19/how-to-spot-and-critique-...
This is not a theoretical problem. There have been ~50 hate killings in the US this year. (And we haven't even had a mass shooting.)
Where judges chose to draw the bar is incidental to the fact that this exception exists. That they chose to draw it where they did is a legal question, not a moral one.
The fact that judges draw the bar rather than you are me is critically important to prevent abuse. Innumerable boorish people would consider calling out their behavior to be "fighting words".
Yet the "you have no right to falsely yell 'fire' in a crowded theater"[1] was an opinion of a SCOTUS justice about a man who was peacefully protesting the WW1 draft, distributing papers arguing for his political ideals. Yelling "fire" in a crowded theater runs a real risk of injury and it's negligent to do so falsely. Telling other people that you oppose a draft does not, yet has not been protected by the 1A (unless the person can prove some religious exemption, as did Muhammed Ali).
As "cut and dry" as we pretend the 1A's protections are, they are far less than what laymen imagine.
[1] https://en.wikipedia.org/wiki/Shouting_fire_in_a_crowded_the...