If you want to peek into oral argument, and actually learn something about the High Court, do yourself a favor and check out the incredible work Oyez does. They mash up the audio with the transcript, and sync it with a highlighted avatar for which Justice is speaking at the time. Having cameras in the court would destroy this medium of consumption, and relegate it to manipulated soundbites and distorted political ads. We should all detest any attempt to change the status quo here.
Here's an example from Oyez. An interesting case that has some good back and forth, and highlights how this really is the best way to consume the history of the court. They have the entire record in there, and their website is very well organized, so you can find whatever case you want.