It's relevant because what you experienced with the "justice" system is a very small minority of cases. As many as 95% of criminal cases end in a plea bargain, with an average of ten minutes or less for the defendant to speak with their public defender. This is before even getting into the suffering within prison. You are significantly more likely to experience abuse from this system if you are non-white.
I see though where you could say for your point that race is irrelevant if you were just showing that the system can be fair, but you say your experience shows we have a "functional judicial system", that doesn't necessarily follow. If it doesn't function fairly in the majority of cases it isn't functional as far as providing equitable justice for society.