As someone from the US - does this mean there are places where students are free to go to any high school they wish? Could this result in overcrowding if all the students want to go to the same school?
Bear in mind that my city has around 100 thousand inhabitants, I don't know if this considered small or medium in US.
I've never heard that we have significant overcrowding issues or somesuch - if anywhere then probably in Vienna, but that's just general capital city capacity woes.
Others are so small and rural that there is only one option, period.
In Boston where there are some VERY good high schools and some meh high schools there is an exam system that may or may not be replaced by something else due to the fact it blatantly favors the wealthier residents.