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.
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.
The commerce clause, and numerous laws leading up to it, were the major opening. It made the lobbying boom possible by giving the government direct control over the economy (and therefore lobbyists acquired reason to lobby, and reason to buy politicians).
All powers not expressly granted to the government were to be outside their province. They switched that, such that any powers not expressly denied the government were to be assumed to be in their province.
What has happened in the meantime is that the civil war and the reconstruction amendments redefined the power boundary between the state and federal governments, but the federal government has not usurped any powers that were originally outside the province of "government" (because there was scarcely such a thing!)
You're trying to argue that the federal government merely usurped powers that the state governments already had, and this is scarcely true. No state ever had unlimited regulatory authority, and no state ever had anything approaching "nearly unlimited police powers"; state constitutions are typically more explicit in restraining the exercise of power than even the federal constitution.