In most cases, school boards had no other decision but to accept students, since they can not stop students from leaving. If the school is at or near capacity, then they can limit or not accept students. Otherwise, not accepting students only reduces your headcount.
The concept that if schools competed for students, then under achieving schools would have an incentive to improve. IMO, this is not happening as intended. Schools that lose a lot of students lose financial resources and a lot of other resources. Taking those resources away does not improve a school system. Again, IMO, open enrollment has done more harm than good to the overall education system
From an athletic perspective, it has created a whole bunch of unintended consequences. Schools with struggling programs find it harder to compete , since kids (and parents) want to play on winning teams.