Not quite. While the window has been narrowing, in 1992’s R.A.V. v. City of St. Paul, even though the Court overturned a statute prohibiting speech or symbolic expression that "arouses anger, alarm or resentment in others on the basis of race, color, creed, religion or gender" on the grounds that, even if the specific statute was limited to fighting words, it was unconstitutionally content-based and viewpoint-based, they nonetheless made it repeatedly clear that the City could have pursued "any number" of other avenues, and reaffirmed the notion that "fighting words" could be properly regulated by municipal or state governments.Fighting words is an essentially dead doctrine. It hasn't been applied at all in more than half a century.
And cases involving the fighting words exception have appeared before the Roberts court. Narrow doctrine? Yes. Dead? No.
It’s also popping up in legal discussions on cyber-bullying.
As for the immediacy test, that applies to incitement, not fighting words.