What an idea. Maybe you should invent a special case for a cell when not in use? That would really be in demand!
They already exist. My husband bought me one on ebay that is a pouch to put your phone in. It blocks everything coming in until you take it out. It works great for church or other places you don’t want your phone to go off without silencing it. We often forget to turn our phone back up after an event if we silence and miss stuff later in the day. Of course you still have to remember to take it out of the pouch.