Umair, I usually agree with what you write, but on this occasion, no. Yes, America is profoundly, weirdly patriarachal. Yes, American patriarchy is appallingly violent and ugly. Everything you say about Trump's narcissist form of it is right.
But. There is another kind of patriarchy.
This is the kind of patriarchy that has a place for female power in its structure, very common in Southern Europe, South America, India. In this kind of patriarchy girls have no power, mothers have a little power, older women, grandmothers have much more power. Often in subtle sideways forms, but the power is there.
Yes, it's a patriarchy - the sexual dimorphism of humans guarantees that. But it's one that is ameliorated by the matriarchy hiding inside it.
American power is a curiously truncated and deformed patriarchy where the women have to pretend to be masculine if they want any kind of power, and therein lies its deadliness.