That's a fair point. I do think it's changing though. My sister is a fifth grade elementary school teacher (she teaches sixth grade math to the advanced class though). She was telling me the other day about how the students are all writing apps for their phones nowadays. I laughed and said, "Haha, no way. 5th graders??" She replied, "Yeah, one girl has been working on an app for organizing health information. She wants to go into the medical field and cure cancer when she's older. Her app lets you input names, body weight, height, and other health information". My jaw dropped. She went on, "It's strange; when we were younger, you were the only one I knew doing this weird stuff. Now they all are."
Granted, she's teaching a gifted class at a top ranked (public) elementary school, but still -- that many fifth graders know how to program for iOS or Android? I was surprised.
So I think your point is spot on. The next generation is going to "grow up to live in a world where we would have free access to educational materials and other wonderful information over the internet." The "could" will turn into a "can".
I understand this because I once ranked in the top 10 in my state for mathematics when I was a kid. So I potentially could have understood specialized maths if they were explained to me, sure, but where would I have gotten that exposure?
When I was in school, there was no Google Scholar or Wolfram or edX. We had EBSCOhost, but the librarian only knew how to pull up old issues of Forbes and Sports Illustrated. My generation's great boon was that we would grow up to live in a world where we would have free access to educational materials and other wonderful information over the internet.
I'm not making this an argument about privilege, but we should deeply consider whether our resources and backgrounds were so typical as we believe them to have been that any child put in our place would have had our abilities.