Here is a crazy idea, but one I have always wondered about. I have not done much umpiring in my life which I consider a wise decision. However I have spent countless hours behind the backstop watching pitchers.
I really got the feeling I could see pitches better from behind the backstop than right behind the catcher. I know I have seen balls and strikes that were called the opposite way. In fact I would bet on it. The wider vision of things just makes it easier to see, especially when it comes to both sides of the plate.
Even if this were true, the other HP umpire responsibilities would make it impossible. I'm sure good umpires would disagree with my theory. But for me, seeing a larger picture makes it easier to see strikes and balls. At worse, I believe you can be at least as accurate as standing behind the catcher. Once again, I understand I might be all wet and that removing the HP umpire simply can't be done.
I think your theory definitely applies to some calls on the bases. I officiated football for many years and we kept a little more distance--partly for self-preservation, partly for perspective--than we do as umpires. I find that the positions I'm trained to be in on the base paths sometimes put me too close to the action, with the play filling up too much of my field of vision. Sometimes, it's good to be right there and see exactly when and where the tag is applied, but sometimes there's too much big movement in the field of vision. I think a banger at first is the play where the dad in the stands is most likely to be right when he disagrees.
I'll have to think about the application of your theory to balls and strikes. I tend to believe that having my face right in the zone is the best way to avoid paralax error and to see whether a non-straight, dropping ball nicks or just misses a corner.