Vandy does not accept based on stats alone. It’s holistic. Nor USC.
“Assuming a kid applies ED, has a 4.0, and a really solid academic schedule, do they have a good chance (>60%) to get into a school with an acceptance rate of ~20%? Given that they don’t have anything that would really hurt their application.”
Absolutely NOT.
Again, these colleges do NOT make decisions based on stats alone.
You have a critical issue with your ECs, aiui. They matter. Any missing aspect can “really hurt their application.”
And even when a kid truly has it all, the school still has institutional needs.