When dealing with Home/Property insurance, always talk to a reputable public adjuster or general contractor. I worked at a general contractor construction company in a state where contractors can also act as public adjusters. We routinely caught insurance adjusters overlooking damage, lying, or straight up committing fraud.
The laws for insurance are very complex, and all of the material standards are locked behind paywalls. For an average person (me before I worked there) insurance is basically a black box; you can't argue against any of their points because they hide the criteria.
>but even if they do fix it, it'll be the lowest bidder installing the cheapest parts possible.
This is true, but illegal. You are owed for "Like Kind And Quality" according to the law. This means that the insurance company can't downgrade your materials, and they have to repair the property to AT LEAST pre-storm conditions. Additionally, it is your legal right to choose a construction crew or contractor of your choice, and the insurance company can't veto your decision. After the work is complete, make sure that you, the construction company, and the insurance company have copies of the specifications of your materials and what work was done. This way it will be much harder for insurance to fuck you over on your next claim.
Most contractors in my area are genuinely trying to help the clients. There are some contractors who take advantage of the innocent and gullible population, though. I hate them just as much as insurance companies.