Why isn't door casing mitered to meet base trim?
The issue is that normally, moldings around a door are very different from baseboard molding. You can easily bevel two identical moldings together; you can't do the same if the profiles are different.

Of course, this begs the question: why are door moldings different from baseboard moldings? Well, mainly tradition; that's the way it's usually been. Lee Sam's answer that "doors are in the wall and baseboards are on the wall" is probably as good as you'll get.