This is getting into a far broader issue, but I feel our society is far too overprotective of minors and in some cases the population in general, largely because of the looming threat of a lawsuit.
This very topic was discussed on another thread recently and your point-of-view seemed to be the dominant one. However, as a non-parent who did many things under the age of 18 which I wouldn't allow any kids of my own to do today, there are times when I feel we don't go far enough to protect minors (realizing that the magical ticking of a clock doesn't automatically transition someone into adulthood despite what laws may enable).
Having had many friends throughout the years who are in such professions as teaching, social work, and public service, I've heard of a number of horror stories (and to be honest, many more which are not even horrific, just eyebrow-raising) about incidents which put young and/or vulnerable people in potential harm. I notice that most of the commenters here have referred to the OP's "parents", but I know from my friends that having under-18s from homes with two parents is almost not the norm, and often the "parent" isn't a biological one but perhaps a grandparent or other legal guardian.
Which is to say that times have changed and the fact that third graders may have taken trains to school unaccompanied or to visit grandparents, etc once upon a time doesn't mean the same practice is wise or safe today. That is not to say that Amtrak's UA policy couldn't be tweaked a bit to make it more passenger-friendly, but I'm actually a bit surprised there aren't more untoward incidents which happen on a train. There are far more places for someone to have something happen on a train and for a longer duration of time than on an aircraft, which is probably the mindset with which Amtrak's policy was written. Yes, it makes it inconvenient for otherwise responsible parents or guardians to do the right thing and get their charges from Point A to Point B without a lot of hassle, but it provides for a greater amount of control and presumably safety.