I think part of what Linus gets wrong is that he confuses the correlation of high-property-tax well-funded districts with the performance of the schools in those districts. The high property taxes (or property values or however the market works it out) doesn't make the schools good, it filters out people who are indifferent to the school quality, and filters in people who place a high value on education. Once you cluster a lot of people with those values, the schools will be good; in part because of the peers a student will encounter, and in part because of all of the small but concrete things parents do to make the schools better.
Open enrollment without tuitions doesn't challenge that clustering. To participate in open enrollment in Minnesota, you have to really value education: you have to figure out what the school is you want to attend, you have to figure out the bureaucracy to get in to that school, and you have to provide your own transportation to the school. All those hurdles are just as good as high property taxes or high property values.
The irony is that as a result open enrollment is not as progressive as it might seem. It's something the privileged can use to fix their children's education experience without moving, or allow people to trade effort for income. But it doesn't bring the underprivileged up, because they really don't take advantage of open enrollment. Though perhaps I'm using circular thinking, as I generally consider children with engaged, informed, and capable parents as "privileged" regardless of income; and maybe I even think that way because Minnesota supports that particular lifestyle choice via things like open enrollment. It's a particular life arrangement that I didn't see much of in Chicago, and maybe that's no accident.