I always thought the Trauma Inn was just an abbreviation for:

• Whew, we're at the inn and can rest...
• ...and the healer can heal us without being under combat stress
• ...and the party gets a good night's sleep
• ...and we can eat which will help us heal
• ...and we can use the spellcasters who work in the inn to help our own spellcasters restore the party
• ...and we can use any healing or restorative items we have on hand that we can't use in the midst of battle...

...except, y'know, without wasting time describing (to say nothing of showing) all that and any other possibility I may have neglected to mention.