not because they cost more to insure, but because the companies my brokers offered with the best rates refused to cover these cars. It forced me to get insurance from companies that didn’t have as good as rates.
As far as the VIN number though, if you give them that info you gave them everything required for them to know it is salvaged. I’m not an expert, but would guess it’s on them at that point if they choose to insure it. I had a company refuse to insure me once when I gave them the VIN because they saw it was salvaged.