First off the courts and police have nothing to do with health care. Secondly, the courts don't dispense "justice", and judges will tell you that first thing as you arrive for jury duty. They dispense the law.
So? We have sewage systems, but their purpose is health. Imperfect systems are how we work toward ideals.
We evaluate the legal system in large part by whether the outcomes are just. For example, the revision of the three strikes law in California is happening because a number of people have received obviously unjust sentences. And we got the law in the first place because many people thought that letting serial offenders free to harm people again was unjust.
"Equitable" is another one of those ideals, and that it is just as subjective as justice or health. But we can work toward it.