Conceptually, how the Constitution works is as follows. The states inherited the sovereignty and unlimited power of the British parliament. In aggreeing to the Constitution, the states delegated some of that power to the federal government, and agreed to refrain from the exercise of certain other powers. The clauses of the Constitution outline the powers delegated and prohibited. All the 10th amendment says is that anything that hasn't been delegated or prohibited hasn't been delegated or prohibited. Which is tautological.
The mere face of the text cannot support an interpretation that the 10th amendment does anything other than state the obvious. If a federal action is otherwise Constitutional, by virtue of falling into one of the delegations, then it is by definition something that has not been reserved to the state.