Earlier quoted context omitted.
I'm not quite sure how your points contradict the parent saying school was about affording the expense. Saying people chose to have kids work for money doesn't seem to contradict that.
I think the last paragraph summarizes it well: "None of this had anything to do with technology not allowing the existence of public education - if anyone could afford it, it was the British Empire at the time. They just had other priorities." Britain had industrialized, had colonies all over the world, went to war with China over allowing to continue selling them opium in this time among other things. Education was…
You can interpret 'afford' as "can literally pay for given any tradeoff" (I can afford a Mac Pro in that sense), or "can realistically make the tradeoffs" (short of cutting my 401k contribution, I don't have the money). Even in the first sense, you said nothing that implies that in the 16th century, the agricultural improvements that grew the population was large enough to spare children from agricultural work. All that population growth implies is that you've escaped the Malthusian trap. Going forward, my sense of the early industrial revolution was that families depended on the money from children's labor, though I could easily be wrong.