something we should nonetheless be concerned about? A law professor argues that the Supreme Court "is the most trusted branch of government" and that its popularity is helped by "the relative obscurity in which the justices work". I'm not sure that the critics of Bush v. Gore would call that a good thing. That is to say, obscurity may help with reputation management but it doesn't necessarily mean that the resulting benefit is deserved. The obvious counter is that greater openness can cause an institution to act more responsibly, rather than relying on its obscurity as cover for poorly reasoned or controversial decisions.
The author accepts the status quo belief that "Justices use oral argument to develop their thinking in a case". Well, no, not all justices do that. Some barely, if ever, participate in questioning. I've heard appellate court judges say that oral argument is influential in probably 10% of the cases they hear. Despite the ostensibly greater difficulty of the cases the U.S. Supreme Court chooses to hear, I would venture that the influence of oral argument isn't even that high. Court watchers are very good at predicting the outcome of cases, which Justices will vote in a given way on a given issue at the point the court agrees to hear the case, even without seeing how the issues are formally framed or reading the briefs. I appreciate that oral argument can influence an opinion and on rare occasions might change a Justice's mind, but on the whole I don't buy into the conceit that you have a significant opportunity to sway the court at that point in the game.
I suspect that it's true that "Cameras will alter the dynamics of oral argument" and "will make lawyers and justices guarded in their exchanges", but I'm not sure that's entirely, or even mostly, a bad thing. Frankly, from the standpoint of the public, most cases are boring. The issues and arguments can be sufficiently obscure that they're boring to most lawyers. Where's the guarding likely to occur? Perhaps there will be some caution in the analogies used in "reductio ad absurdum" questions - those questions that attempt to show how absurd an argument is if taken to its logical extreme. I expect that the Justices are savvy enough that those inclined to be a bit outrageous will substitute theoretical outcomes that won't provoke (similarly theoretical) outrage.
To the extent that a Justice who has a parochial view of, for example, the rights of women, a candid question may reveal that perspective; I don't think that's a bad thing. Justices may be more cautious about questions that make them look egocentric or are designed not to illuminate but to humiliate, but no big loss there. If I may place the onus on the author of the argument, given that transcripts are available, can she point to some questions or an exchange that she believes would not have occurred had cameras been rolling? Any of the questions she fears would, had they been filmed, "live forever on the Internet" and "leave the public with distorted views of the court"? Between transcripts and audio recordings, why haven't we seen even one such instance of outrage - there's been plenty of Internet outrage, after all, at the statements of public figures and politicians that were not caught on video, or weren't even recorded at all.
Also, as fun as "law and sausages" analogies are, the proposal is not to film and broadcast the inner workings of an actual sausage factory. The proposal is to film nine intelligent people who, aided by a vast support staff and bevy of clerks, are being asked to decide really important issues. By the standards of an ordinary American, they are highly paid for their efforts. They are given incredible insulation from public opinion and reaction to their decisions by virtue of their life tenure. How much more protection do they need?
One thing I can guarantee is that the public would not look favorably upon a Justice who is seen, argument after argument, tilting his chair back, eyes closed, demonstrating what appears to be either profound indifference or deep slumber. The public might not like seeing a Justice admonish or humiliate a litigant over a petty issue, when there are serious issues before the court. The public might not appreciate a Justice's questions that, over the course of a case or over time, suggest that the Justice has retrograde opinions on an issue such as gender equality. And whether the publicity causes the Justices to improve their conduct or results in embarrassment for its continuation, I don't see that as a bad thing.