You are correct that none of these analogies carry any weight. The point is not Hizzoner's general fitness, or proclivities, it is whether he could be a fair and impartial judge in an obscenity case. If a random visit to his home disclosed the presence of obscenity or cheap wine, then that fact fairly should be disclosed to those asked to accept the Judge to preside over the trial of their clients. It has to be disclosed, and if a litigant wants to ask the judge to recuse, then they may. To not disclose it threatens the fair and open nature of criminal proceedings.
A closer analogy is if I up on charges for a hate crime, and the Judge was a member of the Hitler youth, then I'm entitled to know that. He can argue its in the past, or his private business, but it needs to be disclosed and his fitness challenged.

The temptation for the LA Times reporter who initially reported the Kozinski story (and his editor) was the irresistible man bites dog quality to “Judge presiding over porn trial caught with porn”, and the related temptation to fudge the description of the porn on trial (characterized as vaguely fetish) and enhance the description of the Kozinski material (bestiality) in aid of drawing a parallel between the judge and the judged.

Now, with the benefit of hindsight and some helpful links, we are all (at least those of us who take the time to look beyond the sound bites) able to judge the alleged “porn” for ourselves.

The portrait of The Times that emerges is less than that of careful journalism.

The man “cavorting with” (a deliberately vague word choice by your reporter that can connote some form of sexual play) an aroused donkey turns out to be a humorous video downloaded from You Tube (which is where I watched it) of a laughing fat guy being chased around a pasture by a donkey with an erection. This is neither “porn”—since it is intended to make us laugh and not to arouse—nor is it “bestiality”.

The porn forming the basis of the prosecution over which Judge Kozinski was presiding when The Times story broke: Commercial videos of women having human excrement smeared on their faces. Not even remotely close to the ribald humor found on Judge Kozinski’s family web storage device.

When the suggested parallel between the judge and the judged disintegrates under critical scrutiny, the story is hardly newsworthy at all.

“Judge found with joke emailed pictures of naked ladies with body paint and other bawdy themes on his home computer”? Yawn.

There are temptations in every profession to cut corners and, unfortunately, The Times reporter (and his editor) fell victim to that temptation in this instance.

Fortunately, the legal Blogosphere—one of the few places Kozinski was widely known, came to the rescue and set the record straight. However, not before the story of the “porn judge” with images of “bestiality” on his computer was picked up by almost every media outlet around the world.

The real shame is, for those who had not previously heard of Judge Kozinski, the “porn judge” story will be their first and lasting impression. That harm, caused by a momentary journalistic lapse, cannot be undone.

However, the point is that the "system" DOES act when its processes are (allegedly) abused.

A full exposition of how the psychodrama of Kozinski nemesis and LA Times tipster Sanai’s dysfunctional family (a key allegation being pressed by Sanai, his siblings, and mother in the Sanai v. Sanai federal court litigation is that the defendant-family patriarch ‘bugged” the family residence for decades) ultimately derailed a federal obscenity trial over which Judge Kozinski was presiding will have to wait.