So, perhaps it is a bit late to be noticing, but a Monk's bonus to speed is an enhancement bonus, while the Barbarian's is not. More often than not, like bonuses do not stack. Since Boots of Striding and Springing and Haste both confer an enhancement bonus, this would mean that a Monk's speed bonus would overlap and not stack with Haste and like effects, while a Barbarian would. Is this correct / intentional?
It is correct, and if I remember correctly, monk speed has been unaffected by haste for several editions, at least since AD&D. The intention would be balance.
ED is correct. Since the monk is a supernatural warrior that is another reason for it.