Compulsory school attendance seems like a different question, and more like an implementation detail to me. At least today school attendance is not compulsory if the parents arrange for the child to be educated up to the currently mandated educational standards. (i.e. Homeschooling is legal.)
(It might be possible to do a comparative study of countries/cultures which have codified educational requirements vs. ones that don't-- comparing basic literacy rates to get some insight into this in the general case. It could be very tricky to factor out economics though. I know what I suspect the results would indicate. But I've not the time to do the study.)
Singapore is a good example in this regard. Its compulsory school attendance law is still less than two decades old.
Letter of Thomas Jefferson to Joseph Cabell, September 9, 1817, reprinted in Writings of Thomas Jefferson (Memorial Edition 1904) volume 17, page 423.
http://learninfreedom.org/Founders_free.html