The ‘learning too much too soon is bad’ paradigm seems categorically insane.

I think most people (including most teachers) don't have flexible models when they think about "learning". When they try to imagine "learning faster", they imagine taking textbooks written for older people and forcing small children to read them. And they conclude that this would be bad, because children need easier texts with more examples and illustrations, etc.

The underlying problem is not seeing the difference between essential complexity and accidental complexity. Some topics are inherently difficult. Some topics are just explained in a complicated way -- maybe because the author of the textbook sucks at writing, or maybe the bad writing feels high-status. What typically happens is that for children, we write textbooks with both low essential and accidental complexity: we teach them simple topics, and try to explain them in a simple way, ignoring status (because small children are low-status). For adults, we write about more complex topics, but also often write in a way that is not optimized for clarity too much, because optimizing too much might be perceived as offensive. Imagine a textbook for adults full of big colorful pictures, with lots of simple examples for everything -- it might be better for understanding the topic, but many adult readers would be offended that they are "treated like kids". I think this is stupid, but you can't fix most adults. However, if we made textbooks for bright kids, I would like to see them made exactly like this.

Yet another problem is that people see learning as a linear process instead of a "tech tree". For example, if you asked "how difficult is it to explain complex numbers to kids?", most people would think about square roots, quadratic equations, then add some complexity about the square root of a negative number... and would conclude that it is impossible. But if you limit yourself to Gaussian integers (complex numbers with both integer coordinates), explaining their addition and multiplication rules along with their geometric interpretation is simple even for a 10 years old. But you have to do it differently than it is typically done at school.

A ‘fast learner’ is really just someone who’s been exposed to this problem/material before, maybe multiple times.

Maybe not exactly the same problem, but a prerequisite for that problem.

In general we have the problem of teaching math in ways that make many students hate math. [...] However, in terms of the math-based disciplines, as long as we are gating on actual ability I think weeding people out here is in principle fine?

I see this as a conflict of interest. The school is supposed to do two things:

teach children knowledge
separate children by their ability

Unfortunately, the easiest way to separate children by their ability is to teach them inefficiently... and then the kids will clearly separate to those who get it regardless of your teaching, and those who don't get it.

(In other words, what from inside feels like "the camel has two humps", from outside feels like "you suck at teaching". There is a concept you failed to explain clearly, some kids get it anyway, some don't. If you explain everything well, you will get a bell curve, not two separated groups.)

Weeding out people by their ability may be necessary in many situations, but you need to make sure your are not making your situation easier by failing to teach them properly.