Accounts of the build-up to the American Civil War put a lot of weight on the concept of balance between the number of free states and slave states in the union, and various complicated wrangling that was necessary to preserve parity between them, deciding whether newly organized states would be "admitted as slave states" or "admitted as free states".
If I understand correctly, whether slavery was allowed in a particular state was not up to the state legislature but decided centrally by Congress. This was somehow tied to a wish to maintain a strict balance between proponents and opponents of slavery in the federal senate. Apparently there seems to have been an assumption that a senator elected in a state where Congress had allowed slavery would (must?) be a proponent of slavery, and a senator elected in a state where Congress had forbidden it would (must?) oppose it.
Was there any mechanism to ensure that each senator's views matched the particular rules that Congress had decided on for the state they represented?
It seems to me that the idea that the federal institutions rather than states themselves decided where slavery would be legal, would have been illusory as long as Congress was in complete balance. If, say, the population of a free state wanted to become a slave state, or vice versa, all they had to do would be to elect one senator who supported the new status, and there would then be a majority in the senate for changing the slave/free assignment of the state anyway.
So why did politicians care, when admitting a new state, whether initially to classify it as a slave state or a free state, if the population of that new state would in practical terms have the power to undo that decision anyway?