I think it depends on the clinic. My final ultrasound ended up being on a Sunday, so another doctor did it. The day of transfer, they were short on nurses, so two doctors did it. Mine and another at the clinic. It was kind of funny, actually. They were shop talking in front of me. "So this is how I do it, with a q-tip blah blah blah, how about you?"
They do the ERs in the morning because 1) they time it specifically to the HCG trigger, which is generally taken at night because that's when it's easiest for most people, 2) you're under anesthesia, and it's less time you have to go during the day without eating. 3) They need time to process the sperm and then fertilize the egg, and 4) it allows you to spend the day recovering.