They don't 'want' to make it 'state legislature based', the US Constitution says that the states make election decisions with only certain federal restrictions! So, the courts really don't make a choice, they just cite the rule by saying that the President has no authority to interfere!
I think that refers to the previous Trump attempt to control election results by having legislatures subvert the will of the voters.
I guess it depends on how you read the sentence and just who the 'they' is in 'they want'! When I read it 1st, I thought courts but, could be either! If it's trump and his stooges, it means one thing, but if it's the courts, then it has a different meaning! Any comment from the original poster?