This looks cool. My biggest caution would be that this effect may be tied to the specific class of data generating processes you're looking at.

Your framing seems to be that you look at the world as being filled with entities whose features under any conceivable measurements are distributed as independent multivariate normals. The predictive factor is a feature and so is the outcome. Then using extreme order statistics of the predictive factor to make inferences about the extreme order statistics of the outcome is informative but unreliable, as you illustrated. Playing around in R, reliability seems better for thin-tailed distributions (e.g., uniform) and worse for heavy-tailed distributions (e.g., Cauchy). Fixing the distributions and letting the number of observations vary, I agree with you that the probability of picking exactly the greatest outcome goes to zero. But I'd conjecture that the probability that the observation with the greatest factor is in some fixed percentile of the greatest outcomes will go to one, at least in the thin-tailed case and maybe in the normal case.

But consider another data generating process. If you carry out the following little experiment in R

fac <- rcauchy(1000)
out <- fac + rnorm(1000)
plot(rank(fac), rank(out))
rank(out)[which.max(fac)]

it looks like extreme factors are great predictors of extreme outcomes, even though the factors are only unreliable predictors of outcomes overall. I wouldn't be surprised if the probability of the greatest factor picking the greatest outcome goes to one as the number of observations grows.

Informally (and too evocatively) stated, what seems to be happening is that as long as new observations are expanding the space of factors seen, extreme factors pick out extreme outcomes. When new observations mostly duplicate already observed factors, all of the duplicates would predict the most extreme outcome and only one of them can be right.