Consider northern Tarrant county of Texas which is the highest density school district area I have heard of.
Houses in Southlake cost about 20% more per square foot and tend to be substantially larger than all neighboring areas except Colleyville. That creates exclusivity largely due to magnified wealth that has grown up around the school.
Now that the population in the area has substantially swollen competition among the school districts has increased irrespective of wealth, though wealth remains an influential factor. When a student can live mere miles from various schools in more than two school districts, in some rare cases 4 districts, there is incentive to consider among the choices even though it’s supposed to limited by geography.
To complicate that further there are state funded charter school systems that have competitive admission requirements and ignore geography.
Yes there are also private schools as well. In many places private schools exist to provide wealthy children a superior education. That does not apply in the north Tarrant area where there are so many excellent public schools to choose from and the wealthy ones are among the best in the nation. In this area private schools exist only to provide education public schools cannot, such as religious sponsored education.