Multiple guitars moving together means multiple necks exposed to the same truck heat and humidity swings, and a long dry move can genuinely warp a neck or crack a finish. Slightly loosening strings for long hauls and carrying your most prized instruments yourself covers the real risks.
Pro tip: Snap a photo of your collection with visible serial numbers before the move for insurance purposes, since a scratched or dinged guitar claim is much easier with documentation.
Watch out: Never leave a guitar collection in a hot truck or car for hours; sustained heat softens glue joints and can warp a neck or crack a lacquer finish, especially on nitrocellulose-finished instruments.