Honest answer? Your question models the perfectionist tendencies that your child is displaying. You’re asking, essentially, is it even worth it to apply, if he’s not perfect? Is he too results oriented, or are you?
Your child has a lot of time to develop the skills that he’ll need to thrive over the course of his life, and you can partner with his current school to help him. You want your recommendation to read something like this: “the family showed great partnership in helping their son develop the habits to thrive in a competitive environment, and we know he’d be a wonderful asset at ______.”