Needmorelego, that is unrealistic, because schools are not evenly spaced among the population. Some people live very close to 3 schools, and others to none. Also, people have free chouce where to live, so many move closer to the most popular schools, making them oversubscribed.
Your utopian vision would require people and schools to be evenly spaced, grid-like, with no overlapping catchments, and quotas on how many children could live in each grid. Instead of competitively applying for a place in a school, you'd have to competitively apply for a house in the grid. It would also require abolition of private schools, faith schools, single sex schools, etc (no bad thing in many people's view, but not likely to happen any time soon).