it is interesting to look at germany here. rules there are different in each region, and some regions have free choice of schools. basically the finding is that in some cases free choice lead to even more segregation in each school because parents avoid schools that have lots of lower class or migrant children. by forcing parents to live near the school the problem is "limited" to the people who can afford to move. so it's swapping one problem for another. the results seem to be mixed however, some studies report that switching to free choice had no effect.