Yes, your thinking about the datums' interrelationship to each other is the reason that A is important. Realize that while we say that datums A, B, and C are all mutually perpendicular, in reality the physical surfaces -- datum features A, B, and C -- might not be perfectly perpendicular.
So picture a part where all of the corners aren't quite 90º -- maybe 89.5º on some and 90.5º on others. If datum A were not referenced, then datum B would become the primary datum, and the fixturing of the part would be flush against datum B (needing a minimum of 3 points of contact). But with datum A invoked as the primary datum, the actual part will be most flush against A, and the actual part might then only touch 2 points on B.
Recall that the hole's position is to be measured from the theoretical datums (simulated by the fixture), not the physical surfaces. Thus, the different fixture scenarios that I describe will indeed result in different position results for the hole from B and C.
With all that in mind, I'm not sure what you mean by saying that tolerance analysis books leave out the orientation idea. Are you referring to tolerance stacks? If so, they don't leave that out, although it's probably assumed by the authors since those books focus on one-dimensional stacks. But please elaborate.