Good point. I call this problem the Giant's Shoulder Climbing Problem. Isaac Newton said he could only see farther because he was standing on the shoulders of giants. By giants he meant all the knowledge amassed by previous generations. The problem is, nowadays the giants got so big, that one can spend the better part of a life just climbing the damn giant, many failing to reach the ever receding shoulders.
I've pondered on this problem a bit before. To solve it, I reached your same conclusion, that we need some breakthrough with new ways of understanding human knowledge simplifying knowledge that is today considered complex, or in other words, we need at least try to build some sort of elevator.
IMHO, the most promising possible breaktroughs I could find were:
(I) a reform in math education, with early introduction of schoolchildren to computer algebra system (CAS) software, shifting curriculum away from tedious manual computations and trick learning. When in university, for example, I learned lots of integration tricks, and forgot most of them a few years later. Would my time had better invested just learning SymPy instead of all those tricks? This idea is pushed by Conrad Wolfram. For example. See his talk at https://youtu.be/jE9lU4E52Vg
(II). a reform of physics education to replace vector algebra with proper geometric algebra, as advocated by David Hestenes. Vector algebra as taught in physics today is actually a hack pushed by Gibbs, that only works well in 3D and demands a lot of shoehorning to work in problems with higher dimensionality. Geometric algebra scales well in any number of dimensions, and many problems become easier. The four Maxwell equations, for example, became one. See the discussion in https://physics.stackexchange.com/a/62822 :
"Now, the contention is that Clifford algebra is under-utilized in basic physics. Every problem in rigid-body dynamics is at least as easy when using Clifford algebra as anything else — and most are far easier — which is why you see quaternions being used so frequently. Orbital dynamics (especially eccentricity!) is practically trivial. Relativistic dynamics is simple. Moreover, once you've gotten practice with Clifford algebra in the basics, extending to electrodynamics and the Dirac equation are really simple steps. So I think there's a strong case to be made that this would be a useful approach for undergrads. This could all be done using different tools, of course — that's how most of us learned them. But maybe we could do it better, and more consistently.
No one is claiming that Clifford algebra is fundamentally new; just that it could be bundled into a neater package, making for easier learning. Try teaching a kid who is struggling with the direction of the curl vector that s/he should really be thinking in terms of the algebra generated by the (recently introduced) vector space, subject only to the condition that the product of a vector with itself is equal to the quadratic form. Or a kid who can't understand Euler angles that this rotation is better understood as a transformation generated (under a two-fold covering) by the even subalgebra of Cl3,0(R). No one here is arguing that that should happen. GA is just a name for a pedagogical approach that makes these lessons a whole lot easier than they would be if you sent the student off to read Bourbaki. Starting off with GA may be slightly harder at the beginning, but pays enormous dividends once you get to harder problems. And once teachers and textbooks get good at explaining GA, even the introduction will be easier."