Has there ever been one? Sounds like a good idea!
I finally figured out the flaw in the concept.
Reality shows aren't watched for their reality-- they're all about the drama, angst, conflict, and hysterics. Throw in some salty vocabulary, a few shouting matches, and some tears. Perhaps a Trump-sized ego or two.
Where in the ER lifestyle would we find any of that?!?
Maybe an ER documentary would be better. We could get Ken Burns to direct the "Mutual of Omaha" guys. We could call it... oh, I don't know... just off the top of my head... "What do you DO all day?!?"
Day 1: (Tense whisper) "Here we are starting out the day with our first ER in his natural (and unstructured) environment. Oh, look, he's going surfing! And now... yes... down for a nap. Wait, wait, he's stirring... there he goes... chores, dinner, and off to taekwondo."
Day 2: "Well, look at that. Surfing again."
Day 3: "Well, looks like he's headed out surfing again-- no wait, he missed the turn! Oh, I see, he's surfing the North Shore today."
Day 4: "Golly, more surfing. How surprising. I can't wait to see what he'll be up to tomorrow."
Day 5: [The series has been canceled for re-runs of "I Love Lucy"...]