Being a tall QB is fine and dandy, but it is hardly a must.
I wouldn't say a must but if you look at the success rates of the good QB's currently and in the past there seems to be many more tall QB's. Even Montana, Steve Young, and Farve were all 6'2''. The other thing to consider is how much the game continues to evolve with monster size players that run faster and that are stronger.
Lamar Woodley - 6'2'' - 265 Lbs
Jack Lambert - 6'4'' - 220 Lbs
Lambert was considered by many as a freak for the team in the 70's. Woodley is considered just a bigger back but more the norm now.
QB's need to be taller to see over their O lines as well....