It took me a few days to watch the videos and read through this article, but I think the main problem with the OP's arguments lie in this "for the good of the whole society" bit.
On the one hand I agree with this in principle, in a world in which lawyers and detectives are working foremost to uncover the truth in any given case. But our justice system is inherently an adversarial one, for better or worse. In the adversarial system, the police and prosecution is working almost exclusively for the plaintiff in a case and therefore against all suspects as well as all those who may potentially be a future suspect in any case that exists or is yet to be created. The goal of uncovering truth is purely secondary, thought to be a natural consequence of prosecution and defense each arguing their side to their best ability. Most of the OP's objections are, I think, rooted in the counter-intuitive nature of this adversarial system.
It's easy to find problems with our legal system. There is a lot of evidence that not all lawyers are equally matched ("buy the best lawyer you can afford" is common advice). A "jury of peers" is very easily misled and influenced by propaganda techniques. This may partly explain why some lawyers are better than others -- some are more skilled with propaganda and rhetoric. This system also is economically inefficient in the sense that it tends to necessitate its own professionals. That's the driving force behind these videos: the audience, legal students, are being told how absolutely essential they are in the legal process, so much so that virtually all communication to law enforcement must go through lawyers. There are also a LOT of cases (anyone have percentages?) where innocents have been convicted, jailed, even executed.
But on the other hand it's very difficult, for me anyway, to envision a system that is not antagonistic and also has as many checks and balances as ours does. It may be a little like democracy, "the worst form of government except for all those others that have been tried." I can't help but suggest that propaganda is also the Achilles's heel of democracy as much or more as it is for the legal system.
There's an interesting parallel between the adversarial justice system and a free, unregulated market economy. In both cases the ultimate goal, truth and justice for one and economic efficiency for the other, is thought to be achieved as a result of individuals working toward myopic or selfish ends. The invisible hand of justice, anyone? Also in both cases real world results show that there are major flaws in the theories. Perhaps these flaws result from simplifications or assumptions that are just not true.