Should this elevated door have trim/casing at the bottom?
I tend to agree that this door would look better if there was a threshold in the bottom of the door opening that included a projection nose out just a smidgen beyond the side casings both in overall side to side length and beyond the surface of said casings.

A door opening like this is a bit of a safety hazard and really should have a "landing" on the low side so that when you are concentrating on getting through the door that you do not get a surprise step up or step down at the same time.