Caplan actually goes through reams of evidence. As an extreme example, in 2008-9 there were 34000 new history graduates in the US. But there are only 3500 historians working in the whole country.
Now, are you trying to argue that history can actually measurably improve productivity in other fields, such as accounting, and it's just the curse of knowledge that prevents us from seeing this?
Also, incompetent homeschooling parents and Scientology schools are hardly the only alternatives to public schooling. One option that Caplan advocates strongly is vocational training. Instead of giving them history classes, let teenagers who chose to do so become apprentice carpenters, there are 900000 of those.