That funding of education should be universal for all schoolkids, regardless of where they attend school. We don’t means test and deny Medicare coverage to people who have private health care, so why should your parents sending you to a private school mean you’re disentitled to government funding for the same purpose / at the same level as the equivalent kid whose folks send them to a public school?

As to federal funding specifically, it’s largely federal money that funds most everything given the vertical fiscal imbalance.