Look at the state constitutions enacted during the 1776-1787 period, how they were created, and what the public discussion of them was. They show a definite distrust of government. (States may have had regulatory powers, but that did not give them license to be tyrannical by e.g. locking people up without trial or conducting unreasonable searches.) Many of the new ideas that were formed during this period about how to structure state government to hedge against tyranny were also used when drafting the federal constitution.

kijin's point stands: back then people did not trust the government (and a key related point: they knew that even a republican (i.e. democratic) government could be untrustworthy). Much of that healthy distrust is gone today.

The federal constitution naturally only concerns itself with defining the structure and powers of the federal government. The "blanket mistrust of government" that you describe was indeed quite present, and is very much evident in the way the powers of the federal government are constrained and circumscribed by its charter.

Of course the federal constitution doesn't limit the power of already extant state governments; it's not the constitution of any individual state. Each state has its own constitution which charters, and constrains, the powers of the relevant state government, mostly in accordance with the very same "blanket mistrust of government".

There was no "unlimited power of state governments" at all; every state in the union had its own written constitution well before the federal constitution came into existence. Most of them are even more restrictive of power, and more vigorous in asserting protections of individual rights, than even the federal constitution is.