No the airline/FAA won't steal your stuff, that's not the concern. The problem is whatever you leave on the plane will remain there until the end of the investigation, which means that you can basically write all of it off for a month. Have the rule say that the airline will be on the hook to return all belongings within 48 hours and people would likely be much more comfortable leaving their things on the place.
It's not rational to try and save "things" in an emergency situation, but neither is a company/FAA just shrugging and saying "you'll get your belongings when you'll get your belongings".