You don't see this at the college level because state universities are run at the state level (and are also funded in an entirely different way, but they do receive state tax funds for in-state students to my knowledge).
I had a friend in college who grew up in an even richer neighborhood, and his school inflated GPAs to the point where most top-tier schools threw away their applications.
Not saying you're wrong, but lack of money isn't the only issue in the public education system in America.
In the US at least, schools bear the brunt of consequence of the lack of social safety nets. They are expected to not only teach but also raise kids that have no real parents (who are either working two jobs or the victims of a life time of poverty themselves)
If we want to improve education, we need to take a broader look at inequality and the cycles of poverty that feed into each other.
You missed the point. More funding won't help if you're placed with kids that do not want to learn. A perfectly reasonable solution is exactly like OP said, separate out at sophomore year the people who GAF. Germany does this, it works well, and it doesn't cost a fortune to try to give students a Stanford level education who just want to do nothing.
There is very little kids inherently want more than to learn—if they've learned not to want to learn, either in general or in the particular venue of the school system, that's a failing of the school system or society more generally that needs to stop happening, rather than writing off those who have been failed.
While I agree that alternative programs should be available, it's a bit silly to chalk up most educational problems to "kids don't want to learn".
Germany doesn't have the scale of inequality the US has and shouldn't be compared strongly to our situation. We have bigger fish to fry.
I also went to a "decent but not great" public school and saw similar behavior. Teachers were underpaid and overworked, and are basically just baby sitters with a lip service to actual teaching. Most of the kids went wild because their home life was so bad and had no rules once they left schools. This is because their parents were working poor, often working two jobs and with no time to properly raise kids. Or trapped in a cycle of poverty that causes all sorts of other home issues.
Most of these problems begin at the home and then cash strapped school systems have to deal with the consequences. Schools have become "child jails" because of broader societal problems.