When I listen to news coverage on NPR of US Supreme Court cases, the reporter (Nina Totenberg) always reads a transcript of the proceedings. This can be pretty dry. I had assumed that recordings must be prohibited.
I have been listening to a podcast* lately about Supreme Court decisions (usually older, more historic ones) where they play back audio of the hearings.
Why don’t we hear audio of Supreme Court proceedings in current news reporting?
Many of the recordings produced by the court are only released in a once per week batch, IIRC on Fridays. But typically Fridays are not hearing days, they are conference days.
From the SCOTUS website:
So reporting on a current case, on the day the case was heard, almost invariably means reporting before the court releases audio of the arguments. Only a very few headliner cases have they rushed the audio to post it the same day as the oral arguments.
And no news agency wants to wait several days for the audio to be released before reporting on a case.
From Argument Audio.
CMC fnord!
Weird. In Canada, the Supreme Court does live streaming over the internet of all cases. Anyone can watch it as it happens.
Why doesn’t SCOTUS?
Who knows? That decision is up to the Justices and they’ve decided not to allow it.
So I presume the reporters are not allowed to make their own recordings?
The various Chief Justices (or is that Chiefs Justice? 
) have decided that to allow real-time video of the Court would encourage the reduction of oral argument to posturing activities, rather than true attempts to engage in persuasion. Personally, I tend to agree with them; all you have to do is watch a small amount of C-SPAN’s Congressional floor broadcasts to see what they fear.