As things stand we have a system where the accused are afforded the presumption of innocence, allowed to defend themselves, are allowed to have witnesses on their own behalf and allowed to have an impartial jury.
Based on several recent cases (George Floyd, Rayshard Brooks, Breonna Taylor and others) there is no question but that a whole lot of Americans are unhappy with that system. Should we change the laws and get rid of the 4th, 5th and 6th Amendments? Doing so would allow all investigation to be conducted through Twitter videos, blogs and chat rooms. There would be no requirement that accusers entertain counter-evidence and no requirement that one accused of a crime be afforded any defense whatsoever.
Would that solve the problem with riots? If we merely sacrificed a few freedoms in an effort to pacify a passionate, active and entitled segment of society that we know has already suffered hundreds of years of oppression would they stop their aggression and be satisfied?
The judicial system could be improved as follows (as yes I know it would require Constitutional Amendments so is unlikely to ever happen). But for the sake of argument:-
1. Abandon the adversarial system of justice and replace with an inquisitorial system of justice
ie: scrap jury trials and replace with a bench of 3, 5 or 7 judges (some trained in things like financial fraud and tax law)
You'd still have lawyers but they would not be able to be showmen for a jury of 12 relatively uneducated and legally ignorant jurors
2. Introduce a third verdict. The verdicts available would be: "guilty", "not guilty" and "not proven"
"guilty" would mean the bench thought the defendant's guilt was proven beyond reasonable doubt, "not guilty" would mean his/her innocence had been proven beyond reasonable doubt, "not proven" means that the burden of proof had not been met and the defendant might be guilty or innocent
This system of justice exists in Scotland Btw, and although a defendant found "not proven" walks, they can be tried again should more evidence arise
3. The penalties for being convicted are too abstract IMO
Justice systems should make the misery of incarceration more transparent.
People should be able to see first hand the consequences of conviction a lot more often on TV and the internet
4. However I believe that once a convict's time is served, they should be deemed to have "paid their debt" to society and have all citizen rights restored
(though clearly a convicted pedophile or a convicted murderer/armed robber should have their access to children and guns respectively, permanently restricted).