Much of your post is correct. I'll just add a few fine points.

I have been a licensed rebuilder here in Illinois for decades. Contrary to common opinion, a salvage designation may have absolutely nothing to do with the condition of the vehicle. And often doesn't. Just one example; theft recovery. The vehicle may not have a scratch on it when recovered, but many insurance companies will 'salvage' it simply to sever any liabilities. They don't know what, if anything, happened to the vehicle during the theft.

There are tons and tons of reasons why an insurance company 'salvages' a vehicle. My neighbor told his insurance company that if they didn't 'total' his son's Camaro after a fender bender, he was taking all of his business elsewhere. He didn't want the young man to have it in the first place. Then there are salvages due to a lack of parts availability. I bought a really nice 300C last year that only needed a rear bumper assembly and quarter repair. But some of the parts were on back order. Then there are repair rejections. Customers won't accept the repair. And on and on. There are so many reasons that a vehicle may get a salvage title. And as I have already said, it may have nothing to do with the condition of the vehicle.

My experience with insurance on rebuilts is that most companies are fine with it. Illinois has issued a valid, negotiable title, and that is all they need to know. But occasionally a company will want an agreed to value, and once in a blue moon, a company will only go liability. But usually full coverage is not problem.