The short of it is that the issue has been decided a number of times, but circumstances could always change. For one thing, there’s the question of who has the power to decide the issue. Certain legislators have attempted to pass legislation either permitting or requiring the Court to accept cameras, but many legal scholars and no small number of Justices regard Congressional meddling as illegitimate. In this matter they hold to the view that the Court and the Court alone decides how best to regulate itself. Consequently, the prospect of cameras in the courtroom has long been a distant possibility, because the Justices themselves haven’t been enthusiastic about the idea.

Of course, this could change, and it may well, since some of the newer members have some more experience dealing with new media, and have expressed a greater degree of tolerance for it.

In another corner of the internet, the very informative writers over at SCOTUSblog.com have taken a run at this issue a number of times, and I’ll do my best to summarize some of what they’ve had to say.

The first post of theirs that I can find dates from Spring 2007, and it references a recent symposium (also partly reproduced here) wherein a number of scholars were invited to debate the merits of televised arguments. In itself, the symposium was apparently organized as a response to a bill which had been introduced by Senator Spencer so as to allow cameras into the courtroom.

For those against, the main arguments which were advanced were that the presence of cameras could prove a disruptive force in a process which best functions in an atmosphere of sober consideration. Opponents argue that the video and audio recording of proceedings would lend itself to sensational news coverage which would take snippets of arguments or statements out of context and thereby create a false impression of the courts work. They are similarly concerned that the intrusion of cameras might lead to lawyers grandstanding so as to make a play for public sympathy, rather than pinning their hopes to the strength of their argument. There is even the concern that the Justices themselves might be turned by celebrity.

Beyond that, some of the other substantive objections which were raised were the risk to a litigant's due-process rights, as well as the safety of the Justices themselves if contentious arguments were of a higher profile and more immediately available to the public.

Whatever the case, before the merits of those ideas can be settled, there looms the question of whether or not Congress has any authority to regulate the behavior of the Court. Here, the consensus seems to be that they do not, as the decision to allow cameras or not appears to be part and parcel with the Court’s recognized and inherent power to “enforce the observance of order.” Even Senator Spencer seems to have acknowledged as much, since as written his legislation simply provided for the Court to accept cameras if they chose to.

At the time this seemed unlikely. Justice David Souter, for example, famously declared that “the day you see a camera come into our courtroom, it’s going to roll over my dead body” during a Congressional hearing. Justice Kennedy has also said that any attempted imposition of cameras upon the court would violate the “etiquette” of government, because “we [the Court] don’t tell you what to do, so you [Congress] shouldn’t tell us what to do.”

Senator Spencer’s forbearance on that matter did not, however, hold. Three years later in 2010 he sponsored new legislation which, if it were to pass, sought to require the Court to televise itself. This prompted an interesting article from Matt Sundquist on the history of cameras in court. Within he noted that while some states (Washington and Alabama specifically) had moved to integrate cameras into their courts as early as 1976, the Judicial Conference of the United States (responsible for the administration of and rule-making for Federal Courts) had trended towards conservatism.

In 1946 they issued a blanket prohibition on electronic media coverage of proceedings which they then reaffirmed 26 years later by forbidding “broadcasting, televising, recording, or taking photographs in the courtroom and areas immediately adjacent thereto.” And, bowing to a 1994 Federal Judicial Center study which showed that cameras may influence witnesses and jurors, Chief Justice John Roberts nodded towards the “the intimidating effect of cameras on some witnesses and jurors [as a] cause for concern” in his order barring them from the courtroom during the highly contested California Prop 8 Trial.

Two of his more junior fellow Justices; Elena Kagan and Sonia Sotomayor, actually disagreed on this point during their senate confirmation hearings. At the time Kagan expressed that she thought “[cameras in the Court would] be a great thing for the institution, and more important … a great thing for the American people” and Sotomayor testified that she had “had positive experiences with cameras.” Later, however, both expressed the same sorts of reservations that were raised during the Michigan Law Review’s symposium.

It should be further noted that both Sotomayor and Justice Breyer participated in trial programs which experimented with cameras in courtrooms when they were serving at lower benches.

Ultimately, which Congress has taken a run at the issue a couple of times since, the final determination will likely arise from within the Court itself, and so far they’ve not shown themselves eager to change. For all the talk about there being a liberal and conservative wing on the bench, when it comes to the formulas by which the Court operates, every Justice seems to be conservative at heart. When asked, their common response references the importance of “careful study,” “serious research,” and concern for the “decorum of proceedings.”

In other words, the issue has not been wholly decided, since it could change at a moment, but as of yet change seems unlikely.

On that subject though, the longtime court reporter Mark Walsh has an interesting perspective. He offers the analogy of audio recordings of court proceedings, and how many of the same concerns were expressed about them. They are now released at the end of every week that the court is in session, a policy which he says “doesn’t please radio and TV reporters who don’t have timely use of sound bites for their same-day reports,” but nonetheless satisfies the desire for access among interested observers.

And, he further notes that, had it but been for the exigency of the Bush v. Gore case, when rapid information about court proceedings was of vital national importance and so same-day audio recording was allowed in a major experiment, even that concession may never have happened. Perhaps it will be the same with television.

Hi OP, just a caution that this sub has a "no current events" rule, so if this occurred within the last 20 years, answers will be off-limits here. Meanwhile, you might consider x-posting to /r/SCOTUS

To answer to your specific question, the logic seems to be mostly that televising hearings would politicize the Court. But the deeper premise of your question is flawed. You can listen to audio recordings of almost every important modern Supreme Court case at oyez.org. You can also access the parties' briefings through various websites. So, the hearings are very transparent.