In theory, sure, I agree with OP. I went to a state school (not even a top one, but the top one for the state, IYKWIM) and turned out
just fine.
Joking aside, I think it really comes down to the individual kid and family and the planned course of study and even the level of interest. It'll also depend on our own financial situation at the time. If we are rolling in it (to be crass), then who cares. If he gets in to a top private, go there! If he gets into a school that seems to perfectly meet his needs, go there! I'd like to believe we will be able to fully fund whatever school he wants and can get into, but shit happens and life doesn't always go to plan.