You're conflating the 10th amendment with the general principle that the federal government must trace its actions to enumerated powers. That principle does not come from the 10th amendment, which wasn't even ratified until two years after the Constitution.
Remember, the Constitutional Convention was a convention to rework the Articles of Confederation. The federal government under tha Articles of Confederation was also one of enumerated powers. That facet was part of the Constitutional scheme long before the 10th amendment.
