I would agree with most of what you say here, but let's reinscribe it a little, as they say.
Heidegger was a right-wing extremist who articulated the philosophy of a movement that successfully seized political power, nearly on a global level. Even after the defeat of fascism, Heidegger managed to use a philosophy that was articulated within esoteric language to infiltrate mainstream intellectual life in every corner of the world.
Sounds to me like he is well worth studying, just like his colleagues Schmitt and Strauss, and far more than his sputtering and incompetent precursor Nietzsche. The fact that there is such widespread liberal naivete that imagines that their work can be separated from their politics seems like an even greater reason to study them seriously.
In any political struggle it does not seem wise to complain that one cannot understand the enemy.