Child labor laws will not end with a ban on farm chores, but if busybodies get their way, they pass through that point on the way to a ban on household chores like washing dishes. Becker (Human Capital) defines "school" as an institution which has education as its principal product. This requires a prior understanding of "education". It also suggests that many institutions that people commonly call "schools" are not schools; failing "schools" primarily produce make-work for dues-paying members of the NEA/AFT/AFSCME cartel and padded construction contracts for politically-connected insiders.
Inevitably, for each child, somebody or some body decides what education that child shall receive. That decision includes the choice of venue (e.g., home, school, farm, or factory). Compulsory attendance statutes, minimum wage laws, and child labor laws put on-the-job training off limits to many children. Compulsory schooling is one particularly expensive and long-lived instance of "industrial policy", the idea that government planners know best where to invest society's resources. Twelve years of State-enforced uselessness benefits no one but school employees.
Update: Over at Cato, Andrew Coulson expresses a related view.