Most of the current legitimacy damage stems from a perception that the Court has members that are arbitrating law over bribery while simultaneously engaging in

Most of the current legitimacy damage stems from a perception that the Court has members that are arbitrating law over bribery while simultaneously engaging in behavior that looks suspiciously coercive. I think that's a major issue, but it's a bit orthogonal to the question of whether they use sound judgment to arrive at rulings like, say, US v. Rahimi 22-915. (The other source, to my eyes, of questions of legitimacy is that the appointment of three judges in a narrow amount of time under one party's dominance of Congress and the Presidency has fundamentally shifted the "flavor" of the way the Court interprets law. Rather than bringing their legitimacy into question, that's rather the point of the process by which the US appoints Justices and the length of their term; the Court's "personality" is stable over long stretches of time, but it can shift and it does go through eras. People complaining about the new era don't seem to realize that for many Americans, the previous era was strange times that called to question in their minds the legitimacy of the Court).