Even if we accept your premise, the vast majority of the lawyers and judges in the world (or even just within the US) are not going to be inside that courtroom, and would therefore benefit from having the trial be transparently publicized. You don't have to get into questions of democracy or corruption or anything like that, your position is just plain factually wrong from the outset.
Furthermore, the idea that the information should be controlled because some people might misinterpret it if they had access to it is extremely totalitarian. You are literally saying "most people are too stupid to understand it so we should just rely entirely on the version of the facts provided by a government mouthpiece," which is entirely the opposite of what anyone in a democratic society should be saying. Should there be summaries of the proceedings so that people without legal training can understand what's going on? Absolutely. But that doesn't mean all of the information needs to be kept under wraps except for what's in that summary, because that would prevent people who do have legal training from fact checking it and holding the government accountable for any lies they choose to tell.
This is blatantly false since people not involved in the legal process would be morons about a legal process. ---