Worked clerical alongside medical staff in a small non-trauma ER for a while (as hands-on as paperwork can get -- I had to visit every patient's room). It's been converted to an urgent care with few changes, if that says anything -- I've maintained relationships with the staff who run it.

It takes three hours because for every individual with a cleanly appreciable and treatable injury, there's someone else who has something very much wrong, often requiring escalation to a more appropriate facility.

I'm sure you can imagine that the process doesn't involve telling someone, "You're in a bad way, so you're not our problem anymore." Assuming the doctor takes the time that you should expect, and works on the appropriate documentation between patients -- not even getting into the work that support staff (both administrative and nursing, depending on the Urgent Care facility) need to do before they can reliably say that they've done their job, there's a lot of procedure that you don't get to hear about between diagnosis reports and documentation, which is explicitly required in the medical field.