It's also liability. If insurance determines frame damage, they're inclined to often total it and settle with you. You ain't getting that car unless you buy it back.
I know this since I've worked in insurance, they don't want to be liable if the car doesn't perform to manufacturers specifications while driving or another accident.
Initial repair/value cost is a determining factor yes, but doubly so future liability. Take it to their preferred shop, repair is inadequate, fails to perform while driving = they're liable for way more than initially.