First, he would be someone the nation could turn do, as they did in the wake of the Challenger disaster. I don’t think we have such a person now.
Second, I would hope he would see the damage being done to science, and weigh in. Not a given as all, and as you have pointed out, he was very much his own man.
I agree, except to add that it’s a good idea to be cautious about such leadership. Although a great admirer of Einstein the scientist (and no physicist can be anything else.) Einstein’s political opinions fell into two — not always mutually exclusive — categories: infantile or dangerous. He was a defender of Stalin to the end of his life, and an apologist for all the outrages of the Soviet Union. I would follow Feynman, if only because he was the type of man who would not wish to be followed.