When I was growing up, I do not recall anyone saying I want to send my child to a school with more diversity. I tended to be the diversity. I was generally the only minority or one of the few in my my classes. I remember being told I do not want to take a home economics course because I would be the only male in the class. I wanted to take it because I wanted to sew, knit, and cook. I also remember being told that I really do not want to take Algebra in the 8th grade because it will be hard. It was. I got a C the first semester. Then I got an A the second.
I have been a teacher for 15 years. I have seen demographics change a lot where I live and work. I hear people say they want more diversity in their school. It tends to be code word for more Caucasians. I do not hear them clamoring for more Latinos, African Americans, Native Americans. It is there are too many Asian Americans and not enough Caucasians. I had a person explain to me they wish there child went to another school in their district because the other is more diverse. Well the one they are at is 58% with the dominant race. The other school is 70% with its dominant race. How is the second more diverse? Well that 70% is white and the 58% is Asian.
School choice? Do you really have school choice? If you have money, you do. The whole voucher thing is fake. Is it trying to send the kids to the more "diverse" school. I am guessing yes.
I think any parent who loves their child would want to send their student to a best school possible. Best school possible will also consider other factors. How is a family with low socioeconomic status get their child to the school outside of their attendance area? It is hard. I took a city bus. I spent hours traveling. Was it worth it? For me, no, I did not get a better "education." I was around more Caucasians though. The school did not have really rigorous classes that I could have taken at the closer school.
It takes a lot to get a student to a school outside of their attendance area and only those with the flexibility to do so will. It could be flex work schedule, multiple cars, etc. Disregarding the quality of the student leaving one school for another, you will still make the fled school worse. Most schools get revenue based on population. With a smaller population, the school gets fewer resources. So, it could lose sections, extracurricular activities, etc.
The real concept is segregation not school choice.