If you choose not to pick up your luggage, it is then processed as unclaimed by the airline. How safe that is varies by airport (for example, thousands of unclaimed bags were stolen at LAX by an organized ring over several years, until it was broken up). Best to have good travel insurance if you do this, though it often has exclusions for deliberately unclaimed luggage. But most airports have plentiful cheap hotel options landside, generally cheaper than the transit hotels.