I think it would go the other way.
Already people can read opinions for themselves if they actually cared about what goes on in the courts. So few do. I don't think there's much actual appetite for using A/V to build trust over what goes on in the Court.
BUT, out of context clips of lawyers and justices mugging for the camera would likely further harm the image of the Court.
Unfortunately, given human nature and the social environment, I tend to agree that that public A/V would only farther harm the image of the Court.
They are only trustworthy if they're actually viewed, and I'm convinced they won't be.
Heck, we can see the nonsense surrounding recordings of Congress to see how that's failed to work out well.
The balance of considerations is a bit different in the representative branch, but the success of using video there to mislead would only be duplicated in the Court.
@volkris @TerryHancock As long as the full recordings are available, they are far more trustworthy for most people than transcripts, especially given that most people read at a 6th grade level or below.