I think there's a lot of room for mathematics education to be revamped to be more iterative and exploratory, which I think would make it appeal to a wider audience. I think that the mathematics community is actually beginning to pick up on this, with the publishing of python notebooks which contain increasingly sophisticated models as you read in to them and provide controls for readers to manipulate the parameter space of the models to explore the consequences of claims, theorems, etc. I think this kind of exploration of the numbers is a better way to learn a lot of ideas than the way I was taught in class, particularly things like statistics, where you can see distributions change as you manipulate parameters.
I figure that in a few years, as people my age who were mostly taught using older methods, but got a little exposure to explore-via-computer learning in university mature, we'll see an increasingly "internet-y" version of teaching methods appear, where there's a mix of video lectures, reading materials, discussion posts/blogs, and interactive models.
Computer programming and hobby crafts are among some of the first fields to make that transition, traditional academics are somewhere in the middle of the pack, and specialized topics like data science are keeping pace with the wider academic community.
tl;dr: I think your point is really just a temporary pedagogical fluke, as we take time to transition our teaching methods.
btw, I used to think like you before I got into math. Its a very valid albeit flawed viewpoint - to think that hey if only there was a javascript doodad somewhere so I could move a slider and manipulate the parameter space, I will instantly "feel" CLT in my blood instead of working through CLT as a dry formal math proof. The reality is, this sort of dumbing things down works maybe in 2D and best case 3D, but beyond that, its utility is rapidly diminished. Also, the results you get in the lower dimensions don't map into higher space. As yummyfajitas points out elsewhere, in a reasonably high dim space, all pairs of random points will be fairly equidistant, which is simply not the case for say 2D. So even the little bit of useful intuition you learn in the lower dims becomes quite useless as you scale up.
Proofs are best learnt by doing proofs. Math is not cinema.
That's really kind of pathetic, and a disservice to your view.
I'd be happy to speak with you, though, if you want to actually read my comment and address a (charitable) interpretation of what I said, rather than your strawman one.
The advantage of this approach is that it works. You can acquire solid intuition this way. But it is arduous as hell and also pretty one-sided - problems are limited to what an average undergraduate can do by hand.
Now, when I think about using computers in math education I don't think of some "javascript doodad" with moving sliders. I imagine instead implementing an algorithm or doing a numerical experiment, learning about possible pitfalls in the implementation, running the algorithm on some real data, seeing it fail etc. I think this experience is pretty valuable too and can nicely complement traditional approach.
As an example of what I am talking about, the book "Structure and Interpretation of Classical Mechanics" (a cousin to SICP) tries to teach classical mechanics with the help of computer programs. But this approach remains unconventional.
Now, I'm not a mathematician or a scientist of any kind, merely a dilettante textbook reader, but I'm not sure that approach is sufficient, or even most efficient to teach all subjects.
I think it arises naturally when you approach subjects where it's directly relevant: engineering, complexity theory, type theory, etc. and people who will need those insights will get them in due time.
But yeah, broadening the audience could help people get a better appreciation of the connections between pure and applied math.