I like that you are using math to model the problem but I think you have to argue a bit stronger on this assumption:
In practice, skills are not independent, but the correlation is weak enough that exponentials still kick in.
IQ is known to correlate significantly with all skills for example. And with N skills you have 2^N sets of skills that could be correlated with each other. I think you have to consider this to argue your point. Note that I think your point likely still holds.
So, one simple model which I expect to be a pretty good approximation: IQ/g-factor is a thing and is mostly not trainable, and then skills are roughly-independently-distributed after controlling for IQ.
For selection in this model, we can select for a high-g-factor group as the first step, but then we still run into the exponential problem as we try to select further within that group (since skills are conditionally independent given g-factor).
This won’t be a perfect approximation, of course, but we can improve the approximation as much as desired by adding more factors to the model. The argument for the exponential problem goes through: select first for the factors, and then the skills will be approximately-independent within that group. (And if the factors themselves are independent—as they are in many factor models—then we get the exponential problem in the first step too.)
I like that you are using math to model the problem but I think you have to argue a bit stronger on this assumption:
IQ is known to correlate significantly with all skills for example. And with N skills you have 2^N sets of skills that could be correlated with each other. I think you have to consider this to argue your point. Note that I think your point likely still holds.
So, one simple model which I expect to be a pretty good approximation: IQ/g-factor is a thing and is mostly not trainable, and then skills are roughly-independently-distributed after controlling for IQ.
For selection in this model, we can select for a high-g-factor group as the first step, but then we still run into the exponential problem as we try to select further within that group (since skills are conditionally independent given g-factor).
This won’t be a perfect approximation, of course, but we can improve the approximation as much as desired by adding more factors to the model. The argument for the exponential problem goes through: select first for the factors, and then the skills will be approximately-independent within that group. (And if the factors themselves are independent—as they are in many factor models—then we get the exponential problem in the first step too.)