I only do interviews in the evenings and on weekends, for all the reasons listed previously.
I have only ever had families do a cold-turkey start. I make drop-offs and pick-ups short and sweet. Mommy and Daddy do not come to daycare. That is how it is from day one.
Hypothetically, if a parent wanted to "transition", I would offer 2 half days (mornings) and then a short day, then start full days.