No, the chart was not from random noise.
1. No they did not.
2. No, they did not.
3. No, they did not.
4. No, they did not.
5. No, they did not.
I could go on, but I think everyone gets the point. You have an ax to grind, and your claims show nothing but your bias.
If you disagree, please post proof of each of your claims.
Um, no, there never were little, red schoolhouses all over the place. Most communities, until recently (last 100 or so years) were happy to have any school to send their kids to, and, even into the 1960s, educational choice was limited for nearly everyone. Heck, it wasn't even until 1925 that kids were allowed to go to private school as a means to complete their compulsory education requirements.
There's more educational choice now then ever in the US.
So, sorry, take your market-driven theology and mis-apply it somewhere else, it doesn't make sense here.