The flip side of the argument is that yes, the state legislatures have the authority to choose how electors are chosen.
Which under certain other interpretations of other voting amendments also may be used to invalidate the compact should it cause a state to assign electors to a candidate other than 1) who the voter (claims to) have voted for 2) who won the vote in their state.
They can make a legitimate disenfranchisement claim which the courts would then have to adjudicate.
A compact that could possibly pass a constitutional challenge all the way around, once the interstate compact issue is addressed, would be to do the Nebraska/Maine apportionment of EC votes by congressional district, and assign the 2 "supernumerary" (senate) votes to the winner of the national popular vote. Although that would create an "interesting" mix of other issues.