Is there hospital choice? In my area anyone who wants to open a new hospital has to get approval from the other hospitals in the area. I don't think this is unique, I believe it's a fairly common practice across the US.
Perhaps, but there's plenty of choice in many places.
I'm in a Boston suburb, and there are at least five different hospitals with 25 minutes of me, and way more than that if I were planning something ahead of time and could go further.
They all advertise on the sides of buses. They advertise on the highway. In the pages of the New Yorker hospitals far from me advertise their brain surgeons, or that they have cyberknife or all sorts of things. It's insane how many ads for hospitals you see if you look.
Meanwhile, our public school system is very good. The teachers are paid well. And a lot of work is done to ensure equity between the schools, so there isn't a "good school" and a school for all the poor kids.
I wish we had the same selection here. I'm in a suburb of Portland and I probably have 5 hospitals within 25 minutes (no traffic) as well, but at least half of those are religious hospitals which do not offer all services. E.g. you hope your pregnancy is smooth if you're planning to get your tubes tied after your C-section, because if you have to go the hospital with a NICU, they won't do the sterilization because they are religiously opposed to it.