This post assumes a very positive view of humanity. It assumes that people aren't studying science in large enough numbers because the knowledge isn't exciting and attractive enough. The alternative assumption is that people aren't studying science because they're thick, or lazy, or both.
In Britain, fewer and fewer young people are choosing to study science at A-level (16-18) and university, despite the increased number of them continuing education after compulsory education ends (16). This is mainly blamed on them choosing to do new, 'soft' options, of which Media Studies is the primary scapegoat (but a Google for 'Mickey Mouse degrees' or a flick through the prospectus of a lower-order university will find plenty of others). This can't be attributed to the non-secret nature of science, because Media Studies is just as non-secret. If the open nature of science was really the problem, it would be a problem shared by every single subject from science to media studies to plumbing apprenticeships, and enrolment would be falling in every subject, not just science.
I don't actually disagree with the main point of the post - that secret knowledge is more attractive - but it wouldn't solve the problem of lack of interest in science. If science went cultish, they would see a short-term increase in interest, but then media studies academics would hide their 'knowledge' as well, and we'd be back where we started. Even if the knowledge was secret I've no doubt that most young people would consider the secret media studies knowledge more attractive than the secret science knowledge. "The chanting isn't as weird, and the robes are better, and even under those hoods you can tell the Physics cult is a total sausagefest."
I think you might have failed to realize what will determine which cult people will choose. When the Media cult makes their presentation, they'll be reduced to showing a movie (or equivalent, maybe a lo-fi virtual reality) and saying "look at this fancy media we can create, wouldn't you like to be able to do that?" But then the Physics and Mathematics cult (I really do fail to see how they could be separated successfully) presents a light bulb, a tesla coil, and possibly a miniature sun and gets to say "this isn't even the half of what we could do if we wanted to. If you want to know how to do it, you'll have to deal with us."
Sometimes I wonder if the Pythagoreans had the right idea.
Yes, I've written about how "science" is inherently public. I've written that "science" is distinguished from merely rational knowledge by the in-principle ability to reproduce scientific experiments for yourself, to know without relying on authority. I've said that "science" should be defined as the publicly accessible knowledge of humankind. I've even suggested that future generations will regard all papers not published in an open-access journal as non-science, i.e., it can't be part of the public knowledge of humankind if you make people pay to read it.
But that's only one vision of the future. In another vision, the knowledge we now call "science" is taken out of the public domain—the books and journals hidden away, guarded by mystic cults of gurus wearing robes, requiring fearsome initiation rituals for access—so that more people will actually study it.
I mean, right now, people can study science but they don't.
"Scarcity", it's called in social psychology. What appears to be in limited supply, is more highly valued. And this effect is especially strong with information—we're much more likely to try to obtain information that we believe is secret, and to value it more when we do obtain it.
With science, I think, people assume that if the information is freely available, it must not be important. So instead people join cults that have the sense to keep their Great Truths secret. The Great Truth may actually be gibberish, but it's more satisfying than coherent science, because it's secret.
Science is the great Purloined Letter of our times, left out in the open and ignored.
Sure, scientific openness helps the scientific elite. They've already been through the initiation rituals. But for the rest of the planet, science is kept secret a hundred times more effectively by making it freely available, than if its books were guarded in vaults and you had to walk over hot coals to get access. (This being a fearsome trial indeed, since the great secrets of insulation are only available to Physicist-Initiates of the Third Level.)
If scientific knowledge were hidden in ancient vaults (rather than hidden in inconvenient pay-for-access journals), at least then people would try to get into the vaults. They'd be desperate to learn science. Especially when they saw the power that Eighth Level Physicists could wield, and were told that they weren't allowed to know the explanation.
And if you tried to start a cult around oh, say, Scientology, you'd get some degree of public interest, at first. But people would very quickly start asking uncomfortable questions like "Why haven't you given a public demonstration of your Eighth Level powers, like the Physicists?" and "How come none of the Master Mathematicians seem to want to join your cult?" and "Why should I follow your Founder when he isn't an Eighth Level anything outside his own cult?" and "Why should I study your cult first, when the Dentists of Doom can do things that are so much more impressive?"
When you look at it from that perspective, the escape of math from the Pythagorean cult starts to look like a major strategic blunder for humanity.
Now, I know what you're going to say: "But science is surrounded by fearsome initiation rituals! Plus it's inherently difficult to learn! Why doesn't that count?" Because the public thinks that science is freely available, that's why. If you're allowed to learn, it must not be important enough to learn.
It's an image problem, people taking their cues from others' attitudes. Just anyone can walk into the supermarket and buy a light bulb, and nobody looks at it with awe and reverence. The physics supposedly aren't secret (even though you don't know), and there's a one-paragraph explanation in the newspaper that sounds vaguely authoritative and convincing—essentially, no one treats the lightbulb as a sacred mystery, so neither do you.
Even the simplest little things, completely inert objects like crucifixes, can become magical if everyone looks at them like they're magic. But since you're theoretically allowed to know why the light bulb works without climbing the mountain to find the remote Monastery of Electricians, there's no need to actually bother to learn.
Now, because science does in fact have initiation rituals both social and cognitive, scientists are not wholly dissatisfied with their science. The problem is that, in the present world, very few people bother to study science in the first place. Science cannot be the true Secret Knowledge, because just anyone is allowed to know it—even though, in fact, they don't.
If the Great Secret of Natural Selection, passed down from Darwin Who Is Not Forgotten, was only ever imparted to you after you paid $2000 and went through a ceremony involving torches and robes and masks and sacrificing an ox, then when you were shown the fossils, and shown the optic cable going through the retina under a microscope, and finally told the Truth, you would say "That's the most brilliant thing ever!" and be satisfied. After that, if some other cult tried to tell you it was actually a bearded man in the sky 6000 years ago, you'd laugh like hell.
And you know, it might actually be more fun to do things that way. Especially if the initiation required you to put together some of the evidence for yourself—together, or with classmates—before you could tell your Science Sensei you were ready to advance to the next level. It wouldn't be efficient, sure, but it would be fun.
If humanity had never made the mistake—never gone down the religious path, and never learned to fear anything that smacks of religion—then maybe the Ph.D. granting ceremony would involve litanies and chanting, because, hey, that's what people like. Why take the fun out of everything?
Maybe we're just doing it wrong.
And no, I'm not seriously proposing that we try to reverse the last five hundred years of openness and classify all the science secret. At least, not at the moment. Efficiency is important for now, especially in things like medical research. I'm just explaining why it is that I won't tell anyone the Secret of how the ineffable difference between blueness and redness arises from mere atoms for less than $100,000—
Ahem! I meant to say, I'm telling you about this vision of an alternate Earth, so that you give science equal treatment with cults. So that you don't undervalue scientific truth when you learn it, just because it doesn't seem to be protected appropriately to its value. Imagine the robes and masks. Visualize yourself creeping into the vaults and stealing the Lost Knowledge of Newton. And don't be fooled by any organization that does use robes and masks, unless they also show you the data.
People seem to have holes in their minds for Esoteric Knowledge, Deep Secrets, the Hidden Truth. And I'm not even criticizing this psychology! There are deep secret esoteric hidden truths, like quantum mechanics or Bayes-structure. We've just gotten into the habit of presenting the Hidden Truth in a very unsatisfying way, wrapped up in false mundanity.
But if the holes for secret knowledge are not filled by true beliefs, they will be filled by false beliefs. There is nothing but science to learn—the emotional energy must either be invested in reality, or wasted in total nonsense, or destroyed. For myself, I think it is better to invest the emotional energy; fun should not be needlessly cast away.
Right now, we've got the worst of both worlds. Science isn't really free, because the courses are expensive and the textbooks are expensive. But the public thinks that anyone is allowed to know, so it must not be important.
Ideally, you would want to arrange things the other way around.