Experience and disadvantages
Jason Roehl in Lafayette, IN
Primer over new drywall is a good thing. With flat paints, it will make successive coats much easier to apply, even years down the road when you repaint. Also, two coats of paint over new drywall won't really cover the difference in texture between the mudded/sanded areas and the areas of bare paper. With eggshell and shinier paints, they won't adhere properly, especially in bathrooms and kitchens, and will damage more easily.
Prime, sand (just a quick once-over with 120 or 150 grit), then two topcoats of a quality interior paint (doesn't have to be the most expensive).
Just a few things I learned in about 20 years as a painting contractor.
Jason