Seer of the tapes! Knower of the episodes!
A judge must avoid all impropriety and appearance of impropriety. This prohibition applies to both professional and personal conduct. A judge must expect to be the subject of constant public scrutiny and accept freely and willingly restrictions that might be viewed as burdensome by the ordinary citizen.
https://www.uscourts.gov/judges-judgeships/code-conduct-united-states-judges
Not that SCOTUS is held to the same code of conduct that all other federal judges are held to, of course.
The value of the DNS is that we all use the same one. You can declare independence, but you’d lose out on that value.