Not a private school experience, but my DD's K experience was extraordinarily damaging due to the kind of severe disconnect between classroom offering and cognitive needs that aquinas describes above. The only differentiation offered set my DD to working in isolation (she's extremely social) with no instruction (self-guided learning is not a realistic ask for a 5yo) while the rest of the class engaged in group activities. To say she was miserable and dreaded going to school each day would be putting it mildly. This was coming from a child who entered K extremely excited to learn, and who had emerged from an extremely rewarding pre-K program where her gifts were fully appreciated - for instance, the teacher allowed DD to take over daily story time.