If a kid isn't college material, he should be sent to a vocational/technology option after a certain age/grade. A kid who isn't college-bound should be learning a skill/trade, or some other terminal option.
That's how most other countries do it. After 8th grade of general education, students are placed onto tracks (there are usually three of them). The first track is an occupational track in which students are groomed for unskilled labor (basically, courses on being polite, bathing, and showing up on time). The second track is a bit more advanced in which students are groomed for skilled labor (like welding, construction, etc.). Students on this second track have the option of going to a two year college which would then make them eligible to enroll at a four year college. And the final track is an academic track which prepares students for enrollment in a four year college.
Students are able to "test up" to a higher track if they or their parents do not agree with the track they are on, but they must pass the test before they are allowed to take the higher level courses. As it is now in Alabama, students who barely passed 8th grade can take honors classes in High School.
This system is efficient and it better prepares all children. Unfortunately, the first hint of it being implemented in the U.S. would lead to left-wing groups screaming "racism" and "inequality," because we all know that a higher percentage of minorities would be on the lower two tracks.
If they knew they had to spend the extra 2 years in class, they might actually absorb more of it rather than just hanging in until they are 16.
When parents receiving welfare money is contingent on the kid being enrolled in school, it doesn't quite work like you would think. Like I said, in the system where I teach, there was a 19 year-old in 9th grade and a 6th grader who drove to school. Free lunches and breakfasts contribute to the problem, because if the parents don't have to pay to feed their little thug three squares a day, they have every incentive to keep them in school.