...Why do we need two different attorneys (one of whom is basically being paid to ignore the latter fact), a judge and a jury to take these facts into account?
Because they serve as reasoned checks and balances against a greater likelihood of error in enforcing law. Consider, the charges begin with the police then reach a prosecutor and even a grand jury before making their way to indictment and then trial. All along that course is the potential for willful or accidental misconduct and error. All along that course the rights of the accused are at stake.
Would you want the doctor who performed your operation acting as the judge of whether the medical complications that arose from your surgery were the result of malpractice?
Of course you wouldn't. And you don't want the same people who charged you to determine the outcome of the charge. So we have an adversarial system. One side presents the prosecution and we have a second lawyer singularly dedicated to making sure the rights of the accused are protected and that the prosecutor meets his obligations before the law.
Then we have a jury, selected to act as an additional check if the defendant doesn't believe he can or should trust a judge (who is by nature of his office more closely allied with the state that charged him) to hear both the reasons and procedure that led to the moment and the answer of the defense attorney who scrutinized every aspect and element.
Re: comic book justice
...I don't think that any reasonable human being (who is even halfway decent and is not a hardened criminal) can read the comics and not admit that the Judge system is better than anything that's ever been attempted so far in human history.
The more concentrated the power in any system the more likely an unjust outcome and corruption. Ours works. And it works in the overwhelming majority of cases. That's why 98% of cases never make trial and of those that do and are subsequently appealed most remain in the verdict rendered.