The problem with the Judicial system is partly a reflection of it's fundamental design, and partly a reflection of current American culture.
Take the design issue. We have an adversarial system rather then an Inquisitorial system. This means that your defense is up to you, the government's sole job is to convict you, and the Judge's only job is to call balls and strikes. Which means that if you're poor in America, and you don't have a lawyer who can go over every single piece of evidence with a fine-tooth comb for Fourth Amendment violations, then de facto you don't have Fourth Amendment rights. The Judge is not allowed to force your lawyer to triple-check that the cops didn't fudge the info they put on a warrant application, your public defender probably only has 8 hours to deal with your entire case, so you're fucked. In France and some other countries the Judge is allowed a more active role, but to do that you have to give him more active role in the investigation, at which point the system becomes an Inquisitorial system. And in the US we're reflexively Protestant, so we insist on remembering the Evils of the Spanish Inquisition (just as Queen Elizabeth I intended) and that's a non-starter.
Note that this means that the only way a Judge has to convict somebody with really food rules lawyers in the US is think his way around Constitutional rights in ways rules lawyers can't counter (for example, the "good faith exception" to the Fourth Amendment says the cop had to know that he was violating the Fourth Amendment to get evidence thrown out) or nobody who makes more then $80k would ever be convicted. The muddle class thinks it always looks innocent, so $80k guy can can easily beat probable cause. But then there's a precedent the guy making $20k can't afford to reason around.
And there's the ridiculous amounts of money we pay people with PhD-level degrees in lucrative fields, and a legal degree (or a Juris Doctorate) is one of those degrees. you make it virtually impossible to give every defendant a lawyer who has a week to devote to his case. The money to pay the lawyers does not exist, the lawyers themselves do not exist, etc.
The "looks innocent" thing is huge. In NYC until De Blasio took office it was routine for cops to stop every young black man in the city once a year on the basis he was pretty sure said young black man had a gun in his pocket and was going to pull it out and start a murder spree. The warrantless search almost never turned up a weapon, does not seem to have ever prevented a murder spree, and was entirely justified by legal paperwork the cop filed when he was back at the station. It resulted in black men into weed losing most Federal financial aid (because they were convicted of drug crimes), including student loans, and thus being ineligible for most colleges. And yet when a Judge ruled that shit violated the Fourth Amendments fairly explicit right to be secure about one's person, she got reprimanded by the Appeals Court.
The basic fact is the Founders took a system that was literally designed solely to protect the Nobility from commoners (in English Law, for example, "Peer" is the word for "nobleman", so a "Jury of your Peers" means a Jury made up of nobleman of your own rank) back in the UK, added some Amendments so their new King-stand-in couldn't use said system to prevent himself from being voted out of office, and called it a day. If you want it to be fairer to people who don't have $250k lawyer budgets you'll need to make good legal help cheap, which probably won't happen unless you change the job market so that people with $250k legal budgets are much rarer. The $250k will get them a very convincing actor with legal skills for the jury trial, and it will get them people with mediocre acting skills to go over the paperwork of the investigation in very close detail and determine what can be excluded, which Juror is most likely to vote innocent, etc. while still having $15k to pay for expert testimony.