I can't shake the thought that all of these came about because of the executive's direct lack of respect for the judiciary, not because of any perception by any executive office that the general population lacks respect for the court. The latter seems to be the takeaway point with these pieces of evidence for past transgressions. I really doubt that more instances of FDR-like behavior will or won't come about because of slight shifts in courtroom decorum.
To make a value judgement here: I think it's a perfectly reasonable thing if courts became more accessible to the general population. Whether it be through relaxed attire, language, or physical layouts -- discarding some of the cultural detritus of rituals of years past wouldn't bring the court system to it's knees because of a lack of respect. Rather, it would show the general population that judicial on-goings aren't some esoteric world that they need to think sacred. (Because really, why should they? The courts are for and by the people.) Accessibility would in turn bring understanding, and understanding would turn the current atmosphere of detachment (re: general public from the courts) into a more meaningful respect.
You start off saying that the general population's respect for the court doesn't matter, but then you end up arguing that changing the rules of courtroom decorum will actually increase the respect for the court from the populace and that would be a good thing.
My opinion is that the general population's respect for the court (in the form of whether or not t-shirts are appropriate courtroom attire) has no bearing on whether or not the executive adheres to judicial decisions. On the contrary, I think the attitude that everyone needs to wear suits in court because "respect the court, or the executive won't" is detrimental to those already marginalized: the poor and less educated. They are probably less likely to recognize the social signalling that the formal attire represents.
My secondary point, apologies for the lack of clarity, is that relaxing courtroom procedures and the mystique surrounding them would allow for greater transparency. Greater transparency and a more approachable set of procedures would allow for greater understanding throughout the general population. A greater understanding of our legal system (my second definition of respect), minus the fluff surrounding it (language, attire, etc.), would be a good thing in my book.
I understand that there is inherent complexity in matters of finesse, whether it be law, engineering, or programming, but I don't think we need to actively propagate stifling behaviors like suggesting that suits (and the equivalent for women) must be worn at all times, forever, in the courtroom.
I don't really buy the point about social signaling. You don't wear a suit to court for the same reason you wear one to a board meeting--you do it for the same reason you wear one to a funeral.
If you want more people to understand legal procedure, you should suggest they read The Illustrated Guide to the Law, a webcomic by a defense attorney.