The only time I used Amtrak there was a child in the opposite seat. Staff put a sticker over his seat announcing that he was alone, which I thought was odd.
Meanwhile round here in London children get free bus travel, so it's very common to see them on local buses, and sometimes trains (tends to be wealthier kids on trains).
Parents can't even let their kids walk to school alone. I seriously doubt they would allow their kids to ride a train alone.