If you ever find a case of a wealthy family moving to a rural area to improve their children's chances of getting into a state school, please let us know.
I went to high school in a science magnet program in Texas. Students from 3 high schools were eligible for the magnet program, and the magnet program was housed in one of the 3 high schools. Our math+science classes were in the magnet program, but our English/history/PE/art/all other classes were in the host school. The program made up about 10% of the host high scool, and students in the program were counted as part of the host school for purposes of university admission.
This understandably made people unhappy at the host school - ~7% of the class is academic high achievers from out of the school zone who take most of the admission spots reserved for the top N%.
I don't know of any cases of parents moving to avoid the extra competition, but I probably wouldn't have heard of that if it happened. I do know of some people set on going to UT who did not apply to the magnet program so they could have less competition.
The point here is you don't need to move to a rural area to decrease school competition. There are plenty of cases where you can move a mile to get into the zone of a less competitive school.
You're losing the forest for the trees. Wealthier parents most often send their children to good private schools, and their children have lots of options for college if they are talented and hard working.
That's a hell of an indictment of the local schools. Where I live (Portland, Oregon suburbs) most middle/upper middle class families send their kids to public school.
This is in fact exactly what happens in Texas. I've met many people who attended UT whose parents or friend's parents did exactly that for the explicit purpose of increasing their chances of their child being in the top 7% of their graduating class so that they could get automatic admission to UT Austin, a very good school to attend compared to the usual options for someone graduaitng #35 in a class of 500 from a public high school with low educational achievement rankings.
They'll often go straight for petroleum engineering if their career path is as calculated during college as it was in high school, and end up with a six figure salaxy at age 22 (not sure this still works as of 2020 given the problems with Houston's gas sector).
For some parents, making sure their child has a sure fire path to the middle class is what they consider their main responsibility, and will do things as crazy as move to a worse school district just to get them on the above track.
If you're as cynical about the value of education (to provide a "job") as the people described, you'll absolutely sacrifice the quality of your kids education (moving to a school with ostensibly less talented or credentialed teachers and possibly less academically gifted peers to learn from and larger class sizes) in order to game the system.
Well, assuming this also moves funding this may actually do wonders for balancing out the system. And there may be some benefits to all the students, in seeing how the other half lives, making more advanced classes available in poorer neighborhoods, etc.
Eh, kids from rich/educated families probably get a much smaller marginal benefit from the quality of the school since they're getting tons of extra stimulation at home (stability, parents reading to them at night, parents encouraging academic pursuits). Meanwhile lower-achieving kids benefit just from having the higher-achieving kids in the same classroom.
They can, but they don't, just like how Jeff Bezos can choose to live under a bridge, but doesn't.
Nobody with money goes out of their way to send their children to a school in a 'common' part of town, because they don't want their children to mix up with 'the wrong kind' of people.