In the USA most places are not densely populated, so the schools are probably already fairly large, and to add an extra classroom won't make too much difference.
Nonsense (I grew up in the US.) There's 50 states so no single system but (except for the old desegregation court orders) pretty much everyone has a "catchment" school - like Scotland. If you move out of your catchment, you change schools.
I raised my kids in London and back in the day, families had a real choice. Most people who wanted got their closest school, or at worse second-closest. A few went further afield - but it was their choice.
The beauty of a true catchment system is that when there's stress, the schools pay the price - not the children. Yes, you get expense and portacabins. You also get fairness for the children and actual choice for families, who at least know what their local school is and have a few years to try to move if they wish - rather than the current system where the unfortunate losers in this lottery are destroyed - loosing their home, their community, their jobs - their entire life gone overnight - because this year, their child can't go to the same school as everyone else on their street, or even another nearby school, but is consigned to a sink school hours away on the other side of the borough. It's unjust, it's divisive, and in many areas it's destroying the sense of community.