Well, whattaya know, a lot of schools are trying to extend the school day, and they seem to be generally pleased with the results. (I advocated doing just that a few weeks ago.) The biggest hangup, unsurprisingly, is funding, and there's some grumbling from various interests (parents, teachers, etc.), but that's more or less inevitable in the field of education policy. The article makes it sound like the people involved are generally happy about the changes they're seeing.
That being said, I would have liked the article to distinguish a little more clearly between extending the school day and adding days to the school year, which are really two very different policy changes with very different purposes, costs, and complications. Very roughly, the primary merits of extending the school day have to do with increasing the amount of time kids, especially those in the lower income brackets, spend being supervised by adults. The educational benefits probably aren't that tremendous, but the sociological advantages are considerable. (Even the article acknowledges this in an off-hand sort of way, saying that "adding hours alone may not do much" "unless the time students are engaged in active learning — mastering academic subjects - is increased".)
Extending the school year, by contrast, has the potential to seriously reduce the amount of knowledge that students lose over their summer vacations - an amount that is currently the equivalent of over a year's worth of school by the time kids finish elementary school. Yes, that's right: kids waste about a school-year's worth of their lives because of poorly-planned vacation periods. (And people say I'm inconsiderate of kids' time!) Unfortunately, the article makes it sound like what most schools are doing is just tacking on another week or two to either end of the school year, which really doesn't do much to address the summer brain drain. What really needs to be happening is a rearrangement of the school year so that students don't have more than two weeks or so off at a time.