We used to live in one of the 贫穷偏僻est 的美国农村

A kid we know in that 贫穷偏僻est 的美国农村  just got in H with likely letter and won the state's presidential award (only one boy and one girl from each state).

It is really up to you and your kids.  Good school helps but not necessary. 

We did felt the HS was not very challenging and moved.  Our DD might hate us for rest of her life because of that move.  At the end, none of my two kids got into IVY schools. 

It is all about balance and your desires. A perfect solution is hard to come by. If you want to give your kids a good fundation in HS, move.  One of you will stay home.  We did that and I believe many other couples did that too.  We don't have things many others do, but we will survive.