While different countries arrived at a rationale for a public education system in different ways, the early rationale for the American system was religious and social, not economic.

The first law mandating basic education in America is known as the Old Deluder Act, passed in Massachusetts in 1642. Its explicit goal was mandating towns build schools to ensure all children within its boundaries could read scripture as illiteracy was seen as was one of Satan's goals. Rationale and defenses for public ed have changed over time, to be sure but the system was conceived long before the American Industrial Revolution.

So, it's a bit misleading to say that at any point in American history, there was a bright line between economic benefit and compulsory education. Instead, it's more likely people point to an economic benefit as a rationale for funding (or defending) a free, basic education.

Certainly in Scotland, there was attempts at achieving mass literacy long before the Industrial Revolution. This was to do with their protestant Reformation - led by John Knox. The Kirk was a Calvinist institution, and so emphasised the importance of being able to read the Bible and in an agrarian country with widespread poverty, education was the best way to achieve this ‘the vertue and godlie upbringing of the youth of this Realme’. Education was to be a joint enterprise between the family, the school and the Kirk. Financial restraints meant that the original scheme didn't quite go to plan.

Alas, the 1616 School Establishment Act shared the Church's expenses on schools with local landowners in rural parishes and burghs. Further, the Act mandated the institution of a public-funded, Kirk-supervised school in every parish in Scotland. The Act would go on to act as the basis for all legislation relating to school establishment in Scotland until the union of parliaments in 1707. In the act, the demands made were:

• Protestantism be promoted and grown everywhere
• Everyone, the youth especially, should be educated in Protestant values - civility, godliness, learning and knowledge
• English should be established as the main (only) language in the land, and Gaelic - a language associated with the barbarism of the Clans in the Highlands - should be outright obliterated.

Thus, this is where I answer your question. Effective or not in the first few instances, there is a clear alterior motive other than any economic benefit at play in Scotland for centuries. For some people, it was a means of securing the reformation in Scotland and to allow everyone liberty of opinion in the scripture. But at the heart of government, education was a way for them to secure a religious and cultural hegemony.