Part of the 14th Amendment to the US Constitution provides that if the right to vote is denied to citizens of a state, that state's share of the US House of Representatives shall be correspondingly reduced. The recent set of GOP state laws and administrative actions to suppress voting seem to me to clearly qualify as such denials. If this argument were found legally compelling it would force a redistribution of House seats; in any case the litigation would force states to defend their actions. Note that the representation penalty does not depend on the voting restrictions being illegal, just that they are effective.
Here's the relevant text from the 14th Amendment:
Section 2. Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed. But when the right to vote at any election for the choice of electors for President and Vice President of the United States, Representatives in Congress, the Executive and Judicial officers of a State, or the members of the Legislature thereof, is denied to any of the male inhabitants of such State, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such State.
Presumably the references to "male citizens" were effectively expanded to all citizens by the 19th Amendment, but that would not really matter for this argument. There may have been some earlier court cases based on this provision during the Jim Crow era, but everything on this topic that I remember was direct action to let people vote rather than penalizing a state for denying them access. Any lawyers out there want to pick this up and run with it?