I hate to play the black card here, but if you don't think it's moot I suspect you haven't been on the receiving end of genuine racial hatred.
As I said, I totally agree that race is a nonsensical construct that we've somehow accepted as real, but some people have accepted it. Some people have accepted it so deeply that they will kill people whose "race" is different to theirs.
I've had personal encounters with white people who weren't going to change their behaviour because somebody sat them down and said:
"Hey, you know what? Genetically speaking there's more variation between people you call 'black' than there is between some black people and you".
In fact, you'd probably get beaten up for even suggesting they had anything in common with us.
What you're talking about is one of those "true in theory, totally impractical in practice" deals I'm afraid. Even of the vast majority of people who aren't hateful, those who are still racist won't change their attitudes because of this education. It's not an intellectual issue, it's an emotional one.
Times are changing of course, but that hatred is something that just needs to be flushed from the system over generations I think. It’s already happening (and maybe there would be value in making it a part of children’s education actually), but unless you plan on sending everyody up in a space shuttle to marvel at the pale blue dot, humanity as a whole isn't going to look beyond these silly little tribes just yet.