Documents don't have intention, drafters do. And drafters are people, who live in a time to which present-day events and realities give their actions context. Those events and realities are different from our own. If they are applicable, then we should apply them as such. If they are not, then we should disregard them. The Constitutional Convention delegates had real concerns about decentralization of power, from the perspective of unrealistic ability to centralize it. They had previously-independent states to appease and convince to abdicate part of their sovereignty, for whom they had to make provisions which did not wholly extirpate that power. Neither of these are concerns for us, and so the intentions of those men on this issue are irrelevant.
Regarding the issue of "balance of power," there was a very real fear by the aristocratic men who drafted the Constitution and ran the early republic of what the Russians would come to call "народовластно," or "people power." They feared an overly strong body politic more than they feared a despot; the "balance of power" you speak of was created not to reign in the power of the state, but to suppress the power of the average Joe, whom the elite Founding Fathers found dirty, stupid, and otherwise undeserving of complete political power. If The People had power, then they could remove their [the FF's] power, and that was too much to consider, even for forward-thinking men as they.