You'll need to cite where this was explicitly stated by the Democrats in front of the Supreme Court.
The lawyer for the RNC, when asked specifically why the RNC has interest in preventing votes in the wrong precinct from counting, well let me just put the question here directly.
Justice Barrett said:
What’s the interest of the Arizona RNC in keeping, say, the out-of-precinct ballot disqualification rules on the books?
The response was that it hurt the GOP otherwise.
Lawyer said:
Because it puts us at a competitive disadvantage relative to Democrats. Politics is a zero-sum game. And every extra vote they get through unlawful interpretation of Section 2 hurts us, it’s the difference between winning an election 50-49 and losing an election 51 to 50.
So they justify keeping a vote in the wrong precinct, which can be shifted as needed to allow a person's lawful attempt to vote alive, from counting is in the RNC's best interests because it helps them win an election.
Justice Barrett allegedly cut him off after to keep him from making his response sound even worse!