Your conclusion isn't wrong, but your supporting argument suffers from selection bias, confirmation bias, and a really small sample size.
Among other things, young people are overwhelmingly more likely to be interested in academic topics if their parents also were (and you can spend arbitrary amounts of time arguing nature-vs-nurture on this; my conclusion is that it's both, and they're usually in synergy with one another on this issue), and statistically that means they are overwhelmingly more likely to be interested in academic topics, if their parents have enough money to *buy* their kids things like books, magazines, and subscriptions to learning-related services (CrunchLabs, Curiosity Stream, Brilliant, etc.) Statistically, the majority of public-library users are below median income, and they're in the public library because it's affordable. Children from lower-income households, statistically, are more likely to check out a video game or a movie, than a book, unless they need the book for a project that someone (usually a teacher) is _requiring_ them to complete (and sometimes they don't even bother then). The kids who enjoy learning, *tend* an awful lot of the time to have access to information that is not dependent on the public library. Though of course there are exceptions. And sometimes there are people who *prefer* to use the public library for ideological reasons, even if they could afford to be independent of it; but such people are in the minority.
For what it's worth, I'm in the same camp as you, someone with a fairly academic bent who grew up relying heavily on public, free sources of information, especially public libraries. My dad had a graduate degree, but it was in a field not known for large salaries; my mom, who is no dummy but doesn't have a bachelor's degree, was actually the primary bread-winner throughout my childhood. (She attended a hospital-run nursing school, back when those were a thing, and so was a registered nurse.) But, statistically, we are in the minority on this.
With that said, it's absolutely true that lack of interest in information, is a much bigger problem than lack of access to information, in the modern world, especially in the developed world.
