I see your point, but actually I disagree, despite the fact that I would have _loved_ this idea back when I was in school. Its a cultural problem, but not one thats been noted so far. The issue is that _parents_ in the U.S. do not value their children's education as much as in other countries. Its far easier to plop a kid in front of the TV after school all day then keep a child motivated in his studies -- this requires extra effort on the parents' part. We can blame the sucky public school system all we want, but the fact of the matter is that parents who take an active role in their child's education have a profound effect on what the child gets out of it. Those that don't spawn the next generation of the lower class, period.
Of course, there are cultural issues that prevent this parental oversight from happening, and _that_ is what needs to be addressed. Americans on average put in more hours per week of work than nearly any other 1st world country. Couple that with single parent families, parents that work multiple jobs, and the myriad of other issues that (un)reasonably prevent parents from taking that active role in their child's development -- and well, its no wonder we're in this sorry state of affairs.
The solution is _not_ to throw more money into the education system by extending the school year. The solution is forcing parents to be accountable for their childrens' development. But to be real, we'll probably vote to extend the school year to get a few more weeks during the summer where we don't have to pay a _real_ babysitter.
Or, for the tl;dr; crowd -- School alone doesn't make for good students, parental involvement does.