Would that not utterly stratify social classes? Upward social mobility would be near impossible if not for general education?
Children would have no approaches other than what their family already has access to. The son of a smith becomes a smith, the son of a carpenter becomes a carpenter, the son of a lawyer becomes a lawyer and so on.
And schools also function in part as day care. Parents can devote hours of the day to work, focused and without worry for their child. If all parents had to bring their children to work, would that not diminish their ability to work?
Can an electrician focus on his work when a young child is with him? How can he teach the child the theory of electrophysics that is necessary to understand if one is to become an electrician? Do others at the site watch the children and explain the theory? Would you then not end up with teachers again?
Edit:
This is also a rather amerocentric take. What of other countries educational systems where you can choose more directional high schools. Where the final year of highschool IS an apprenticeship in some vocation? Where you leave school, with no debt and with experience on the job.
And all the countries where education is free. Countries where relevant experience is a part of the degree? Where courses in teamwork, leadership and other skills are a part of higher education?
To discard educational systems because of the defects of a single country's defects seems poorly thought out.