you assume poor people are idle.

I don't assume anything. I just point out, that cost of self-education is indeed huge, if you measure it in profits not received from performing some labor. However, its 'price' would still be on par with being completely idle. Of course, not all poor people are idle, but some are. And if those who are indeed idle can afford idleness, non-idle people may afford self-learning.

What's the cost of self-education of a person that doesn't much anyway? Sitting on a bench all day is not labor, it's a waste of time.