> The closest thing to "settling" a criminal case is to take a plea deal, meaning you do admit guilt, usually in exchange for a lesser sentence than you might receive if found guilty at trial.

In most US jurisdictions you can actually "plead guilty" while still maintaining innocence. It's called an Alford plea, and it's basically saying, I didn't do it, but if we went to trial you could probably get a conviction based on the evidence you have, and I'd rather take the plea deal and reduce my sentence.

It's an important thing to allow because you shouldn't have to admit guilt if you aren't guilty, but you also deserve the same ability to reduce your sentence as somebody who pleads guilty. Why would you want to accept a sentence when you are innocent? Well, the system isn't perfect. Sometimes the police fixate on the wrong suspect and fail to investigate everything. Sometimes the evidence is misleading. And while the law requires proof beyond a reasonable doubt, sometimes genuinely unreasonable things happen.