You are right it may or may not be a deterrent. But, it won't be pleasant for them mentally. Not, getting the fame they think they earned. Being cut off from the notoriety. Very good psy ops. I would extend this rule to any suspected killer though. They don't need to know what is being said in the media. Let em wonder. Let them get all their info from their lawyer, but only to the extent of what they need for their defense case.

you wrote:
(I use the male pronoun noun to ignore a possible woman shooter, but because such a case is rare if non non-existent.)

but I think you probably meant to be fair and write:

(I use the male pronoun noun NOT to ignore a possible woman shooter, but because such a case is rare if non non-existent.)

At least that's how I read it.

One of the standards of competence to stand trial is ability to assist in your own defense.

A proposal to limit what defendants can know about their own case while being held awaiting trial...

It's a new low.

His attorneys can tell him what he needs to know for his defence: "Some say that you did X, can you respond to that?"

They will know, far better than the suspected shooter, what he needs to know about his case.

(A "new low" not to let someone gain what he desires most after possibly killing a number of people? Hmmm . . .)

On edit:

What the news media knows about the crime is much less than either the prosecutor or defence knows and is often inacurate (like Holmes mother presumably saying "You have the right person" when taking the call from ABS News).

I'd like to "run it up the pole" as a real possibility.

And it could be extended to suspects of other crimes where notoriety seems to be one of the most significant motivations for the crime: assassination, etc.

And a question: are all inmates given the right to have unlimited access to television, newspapers, the internet, etc.? If not, questions of legality might not be pertinent.

The suspect's lawyer(s) could, of course, provide the suspect any information they thought relevant to the aid in his defense with no qualification.

But what decent attorney would give him information for the sole purpose of allowing him to wallow in his notoriety? That would be feeding his disturbance and counter-productive. That is, the "aid in his defense" would be colored by an continued unhealthy focus on his public profile.

(This completely in jest, of course.)