In my opinion, "involved" parents means educated, empowered parents. We are in a sense the guardians of the school system, and when we vanish, the schools go downhill.

It's not just helping out in the classroom and joining committees. Educated parents know what good education looks like (or at least, we have an opinion in the matter). We know when to demand better. We know when we need to thwart a pedagogical fad. My hometown school eventually adopted algebra in 8th grade, and calculus in high school, because a few parents hounded the school board. Simply by being around, we see what's going on. To be fair, we also support school programs when they work. And we also know how to demand resources, for instance by supporting funding referenda at the local level.

The problem with schools in the US could be expressed by saying that somebody has to stand in as the guardian of the schools, but we don't know who or how.

IMHO, it's because bad students are like bad apples: they spoil the entire barrel. Randomly mixing your students ensures that every school has a fine selection of each of the types of bad students, with the expected result that every good student's education is negatively impacted.

Selective schools, OTOH, can attempt to select against bad & disruptive students.

Lack of parent investment and activity in school functions because the school is 40 minutes across town (in a city that is hostile to car use). Oh and if you have multiple kids, they can be sent to different schools.

If the parents are upset, they won't be involved and you get bad schools.

I don't understand why this would be the case either. Even if all the rich people send their kids to private school, there is still a middle class population who will not be able to spend $30k a year to send their kids to private school. Plus, not all kids will get selected to go to school across the city from where they live. Some portion will randomly be selected to go to school nearby, so their parents can attend events. I am not saying the random selective policy is good or bad, I just think universally bad schools has to be the product of something else. Perhaps just general bad management of the school by the superintendent?