Let me start by staying, I don't think it's absolutely out of the question that this could happen. It would be hard to argue with placing Harper on the Opening Day roster if he hits .300 and 10-15 homers in Spring Training against real Major League pitching.
There have been a few players in the modern era to make the majors before his 20th birthday with success, so it wouldn't be unprecedented. Although, I'm not sure Harper wants to model himself after Alex Rodriguez (see: steroids). But regardless of what Harper is able to do with the bat, there is a significant amount of development left for the immensely talented 18 year old.
Despite Harper's proficiency with the bat in front of the junior college circuit and a short stint of major league pitching, it will take months to determine how he will adjust to Major League pitching and continue to evolve at the plate. It's an easier road to climb to try to do that while working up through the minors, rather than being thrown into the majors immediately.
As a fielder, Harper has played several positions throughout his young career. During his short time with the College of Southern Nevada though, he was predominantly a catcher. The Nationals drafted him as an outfielder, and he will need time to develop those skills as well.
Bryce Harper is an unbelievably talented, young baseball player, and the organization is rightly excited about his arrival in DC. But there's no reason to rush Harper's development when he could take his time and truly become the player everyone expects him to be come, and do it the right way. I think Mike Rizzo and Co. recognize that. It seems unlikely that Harper will break camp with the Big Nats, though it will sure be fun to watch him crank home runs over the space shuttles in Viera.