Years ago, I sent my mother-in-law our old computer when we upgraded, and I made sure to include kid-friendly software on it so my very poor nieces and nephews would have reason to get on their grandmother's computer when they were at her house. I saw this as a very important element in trying to make sure they didn't wind up on the wrong side of the digital divide. At the time, computers were not nearly as central to modern life as they are currently.
http://www.coding2learn.org/blog/2013/07/29/kids-cant-use-co...
https://news.ycombinator.com/item?id=13506283
You'd have to curate the experience to do something that forces them to learn necessary skills. I've seen those skills dressed up as games or something on occasion. Most fun apps don't do that, though.
The parents seem to have some vague concept that spending hours each evening on Facebook and YouTube will impart, by some sort of cybernetic osmosis, a knowledge of PHP, HTML, JavaScript and Haskell.
And you posit that their computer literacy will go up if we start throwing them off the public computers so they can't even use Facebook and Youtube?
Your argument that they aren't so hot currently in no way rebuts my assertion that if you start throwing poor kids off the internet at public libraries they will be left even further behind than they already are currently.