Door casing is designed so that you can use a smaller trim nail on the outside edge of the trim. The smaller trim nail at the thinner edge helps to pull it tighter to the door...

... and larger casing nails on the outside to secure the trim to the underlying studs...

I have worked around many old timer carpenters and had to learn to do it their way. I still prefer the old style professional approach to installing trim and use hand drive nails. However, some choose to use air brad nailers. I don't like these because they allow the trim to move which can cause cracks in the caulking. The most common problem with this method is the wood splits. You can tap the edge of nail with a hammer to dull it and it wont split...

Door casing also looks nicer because the design places the focus inward toward the door, as opposed to the plain flat look of floor molding.
Standard Zamma Base Molding is about 9/16" thick. Standard Woodgrain Millwork Door Casing can be as thick as 11/16" and Fypon Door Casing which is a very modern look and is an inch thick. Therefore, using baseboard means you will have the same thickness on the floor and around the door, which will look strange.
If you are using a pre-painted baseboard; the bottom of the trim is usually not finished because that side is meant to be against the flooring. When you use it as door trim, the bottom would be facing outward. MDF doesn't accept paint very well so you will have to use a primer. After you apply your trim paint, the outside edge will appear different. You would also have to sand it to make it as sooth as the face of the trim will be.
Can you use it? Of course. It's your home. I wouldn't suggest it. Most people that go this route eventually change it.

