The fact that SCOTUS justices aren't bound by a code of conduct is troubling, and reforming the courts to change this reality shouldn't be a partisan issue. However, even if legislation is adopted, it won't fully rectify the court's continued issues with credibility. Ethical lapses are only secondary to the reality that SCOTUS' public opinion rating has been tarnished as a blatantly partisan institution manipulated by Republicans in recent years.
Since the swing towards a conservative and originalist majority in recent years, SCOTUS has faced a cynical and sustained campaign by the left to undermine its every move. Certain questions of the judiciary should rightly be asked, but this coordinated attack, which ignores examples of the exact same behavior by progressive justices, is wrong. The current Democratic crusade is simply the angry reaction of activists who no longer have a majority of pliable justices whose wills can be bent as seen fit.