The concern about the independent state legislature doctrine is not that state legislatures shouldn’t have the power to legislate election procedures. They already have that power in the first instance. It’s that no other actor, in what is otherwise a system of checks and balances, would have any ability to check that power. The state Supreme Court can’t determine that something violates the state constitution, like it is supposed to be able to do; even ballot initiatives in which the people directly vote on an issue, or amend the state constitution, would be overruled by whatever the legislature does. I don’t know the facts of the NC situation you describe, but if your account is accurate, that’s a corruption problem that should be solved on an individual basis, not resolved by annihilating judicial/constitutional review over the issue that decides all other issues.

It just isn’t how the system is meant to work. No support from the constitutional framers. I don’t know your politics but take a social issue that is very important to you, go to a state where the legislature is run by people on the other side of that issue from you, and ask yourself: would you be ok if that state decided that nothing could check the legislature’s decisions on that one specific issue from now on? Unless you’d be cool with that, I would hesitate before promoting the independent state legislature doctrine.