Many of those whom have survived such a scheme (assuming the course
really is hard) have stories of how a class of 50 bright and
enthusiastic hopefuls is reduced to 10 or so tired dogs.

This is probably because there is a huge rift between "getting"
(appreciating and manipulating) math, and knowing how to put it to use.
I can easily plot some data with tools like Incanter or R, but fail to
even be able to intuitively comprehend something basic like a proof of
Rolle's Theorem or the Significance of Lagrange's Remainder.
[1]

My personal love-hate relationship with math:

You go on for hours racking your brain over some difficult problem,
during which the world transforms between 60 million different colours
and new wellsprings of revelation are found, teasing you with
increasingly accurate semblances of its final form, before finally
reaching a climax with a few simple strokes that bring closure to the
problem. You go to bed proud of your accomplishments and feeling like
the King of the World.

You wake up the next day and realise that not only do you not know how
to make use of the knowledge gained from solving the problem, but you
also can't fully remember how you even solved the problem in the first
place.

Those people who can really appreciate the true beauty of Math are
addicted to the experience described above, but without the lingering
regret.

Footnotes:

[1] - One thing which I do like to do is ask some of my
professors for an explanation of the Central Limit Theorem, and to
observe the different kinds of responses.

Some of them reply in a very 'Mathematical way', which you know once
you hear (the word 'epsilon' is featured heavily).

Others use a 'layperson approach', starting with the purpose of the
theorem, then talking about how one could run a simulation (like a
series of fixed number of coin flips) and see that something 'simpler'
like a Binomial distribution resembles more closely a Bell Curve as
the tests go on. They then show you the math, simultaneously extending
it to something different like a Poisson distribution. And by the way,
here's something you didn't know about Jensen's Inequality...

While that example exemplifies the divergence in pedagogical styles
(guess who is more effective), I conjecture that it also reflects a
divergence in the mode of thinking between the professors.