The basic premise of the Constitution was a separation of powers and a system of checks and balances because man was perceived as a fallen creature and would always yearn for more power.
The whole basis of the Constitution was a restriction of power, and the whole basis of the federalist system was that there was not one sovereign centralized power from which all authority flows.
Acknowledgment of God is not now, or ever has been, a violation of the US constitution.
Power's not what the Constitution was about.