Wisconsin is exempt because it offers Election-Day registration. The exemption relieves the State of a federal duty; it does not impose a unique burden that violates equal sovereignty. The NVRA rests on the Elections Clause, not § 5 of the Fourteenth Amendment.
Congress has broad power over congressional elections. Equal-sovereignty rhetoric does not convert an explicit statutory exemption into a constitutional violation.
List-maintenance fights are increasingly fought in court instead of in legislatures. This decision limits one avenue for private organizations to conscript federal courts into those disputes.
Bottom line: A private group cannot use equal-sovereignty arguments to override a clear statutory exemption. And so much for the argument that that the Federal government is interjecting itself into state-level elections activities to “tip-the-scales” for certain candidates.