Gosh. Your stubburnness is truely appreciated. There are two things. First, if you don't have full coverage then you are out of luck so that the only place you can get redressed is through court. Second, even if you have full coverage, you probably need to consider the premium increase as well.
If you know the insurance matter you should also know that insurance and law are two different things and one thing does not bar the other. I am talking about law and you are talking about insurance. That is why I said you were talking about different things and you would not admit.
In law, insurance is categorized as collateral source payment. The amount of money you get from insurance does not bar recovery through legal system. For example, if an owner in New York City contracted with a contractor to build a hotel and specified time of the essence because he did not want to lost any New Year's Eve guests. He separately INSURED for 5 million dollars if the contractor did not finish on time. When the contractor did not finish and resulted in 5 million dollars in loss of guests, how much compensation would he get? As you said, no need to sue anybody, just file a claim to your insurance company to get your 5 million dollars back. While, the answer is WRONG. The correct answer should be not necessarily. Courts are split on how to treat collateral source payments. Some courts will take the defendant' view that the owner should not be double-compensated because he only suffered 5 million dollars loss. There are also other courts taking the owner's view that the owner paid premium for the insurance, although he could get his money back from insurance company, the defendant was not penalized and he was unjustly enriched by 5 millon dollars. If you are in a liberal state like CA, NY, and MT, well, good luck, because you can recover 10 million dollars, all combined, 5 from insurance and 5 from the defendant.
Again, insurance and court are totally different things. If you are the insurance agent and tell your client to file a claim instead of going to court, well, that may be malpractice because your ignorance of law. One thing does not necessarily bar another. Do not ever assume one way is on top another. There are also many other ways to settle disputes, arbitration, meditation and they are all working together to settle disputes.