The fact that the people of a territory may have voted to be admitted is Constitutionally irrelevant. Colorado and Nebraska are only two examples of territories that petitioned for statehood but had to wait, in Colorado's case for years. The act that creates a state is a vote in both houses of Congress. If your point is that leaving should be through the same method as joining then wouldn't such a vote have been needed by at least 5 of the original seven Confederate states. Or all of them?
...it is under the assumption that they have read the Constitution and agree to its rules...
The Constitution is silent on how or whether a state may secede.
If the states back then weren't looked as as individual entities, then why was the expression, 'The United States are' instead of 'The United States is'? Big distinction, according to Shelby Foote and other historians.
States are still separate political entities. But that doesn't mean that they can do whatever they want. Especially when their actions may affect the other states.
"Sovereign" means "sovereign". "Reserved powers" are reserved -- and so stipulated by the Tenth Amendment, which was the make-or-break amendment for ratification of the Constitution in the first place (thus constitutional historians).
No, Ohio does not get to tell Massachusetts they can't secede from the Union and start their own country with five or six other States (in fact, I wish they would).
Secession did not impair in any way the continued enjoyment by the other States of their advantages in the Union. What it potentially meant was that rather less cotton money would stick to Yankee paws. That's why the Yankees went to war -- money! Their highest principle <spit>.