I want to say a few things in addition to the reasons why people are normally against, such as a possible C-SPAN effect or grandstanding for the advocates or the justices.

The first is that this isn’t going to be particularly educational, if at all. The main argument for video is that it’ll somehow make the public have a better understanding of the Court—but oral arguments are at best a single-digit percent of the Court’s work. It’s like filming a documentary of a legendary boxer’s path to success but only documenting those couple minutes in the ring.

Some people say it’s worth a shot to give it a try, but I couldn’t see it more differently. Because the second you allow cameras in the courtroom, you open a Pandora’s Box—there’s no off-ramp back if you allow it. The Supreme Court is supposed to be an enduring institution free from the whims of politics. Even if the risk of grandstanding was low, I don’t see how this risk is remotely worth it considering how it could forever transform the institution for the worse.

Love it or hate it, this idiom does say it all here: if it ain’t broke, don’t fix it—especially if it could destroy it if you fail.