The irony is that most educated people living in small towns want to get outDoesn't seem like you know much about small towns. I grew up in one. The educated people are there because they want to be. That's sort of by definition, and follows from the fact that they're educated -- they have been somewhere else (you don't get "educated" in a small town, not in the way you mean), and they chose to go there.
The ones who want to leave are the uneducated ones, who would love to have an opportunity to get "educated" in that sense.
Your kids all else equal will be outsprinted by kids who live in more competitive cities
Not everyone wants to be part of this rat race you're talking about, nor do they want their children to be. Having ended up at FAANG (despite my small town upbringing), I talk with a lot of young people (interns, new hires) who are products of this rat race. By and large my impression is that:
1. They haven't lived much. They haven't done many things. They've been too busy in their competitive classes in competitive schools trying to get into competitive schools.
2. They don't seem very happy. They tend to be high strung. Nervous seeming. Scared of failure.
that decision will ripple through to future generations, e.g. your grandkids will be less educated.
How would you even know this? How do you know parental education status isn't the real factor?