Insurance companies will request the police reports and any supplementary documents from the investigation (citations, reconstructions, total station data, etc) and will use that in their evaluations to determine fault and liability in crashes.

It's a common misconception that police determine fault in a crash - they don't. Insurance companies (and sometimes court proceedings) determine fault and assign liability. Law enforcement investigates, documents facts, and enforces the law. The citation is an important part of fact documentation and enforcing the state traffic laws. If there is probable cause in a crash that a law was violated, the issuance or non-issuance of a citation will be used by the insurance companies in their evaluation - and if no citations are issued in a case where probable cause existed, it can really leave a party out to dry insurance-wise in some cases. Some crashes may have been caused entirely by one party making an illegal maneuver (ie. lane change into an occupied lane, a common one), and yet if the report/investigation is generic and no citations are issued (given that evidence existed amounting to probable cause of a violation existed in the lane change violation, and the officer elected not to cite), an insurance company may assign 50/50 fault in that case - really unfair to the driver that violated no laws.

When I did crash investigations, I had depositions where the fact that I issued a citation (and accompanying evidence amounting to probable cause) was critical to the civil case in the crash. I've also testified when I did not issue a citation, which was always because there wasn't probable cause of a violation. It's not fun at all to issue a citation to someone after they have already crashed (as you said, the crash itself is significant punishment), but it is a very important part of due diligence for a good investigator and law enforcer.