This idea is one of my most obvious, so I had the most hope someone else had/found the idea and realize it:
earbuds; these tiny things that free up a hand, get lost or empty. With a special phone case and interaction however ...
What if you could change:
phone rings, touch "accept", talk about something on the web, as you want to look at the screen and keep talking you, you start the search for your earbuds and when you finally find them, they're empty ...
into:
phone (case) that holds and charges the earbuds and answers the call when taking them out
Already realized variation: https://mobile.twitter.com/LanceUlanoff/status/1214645369084116992
BTW: for answering the phone call without earbuds, an idea: touch screen IN the middle answers, touch screen near the sides denies it.