[jerf]

"With the former you’d expect a normal distribution (not uniform) due to the central limit theorem"

You'd expect it, but in the real world you'd be extremely frequently wrong. Correlations in the real world very frequently end up defeating the central limit theorem in practice.

The central limit theorem, being a mathematical thing, is correct; it can't be "wrong". However, while adding together a lot of distributions will absolutely trend towards a normal distribution, it does not make very many promises about how "quickly" that will happen. In practice the real world is filled with the sort of pathologies that result in it being "very slow". Scare quoting some words here because they are rather vague in math terms and I feel bad about that, but putting real mathematical meat behind them would be beyond the scope of an HN post. Many, many, many things are not normal that "should" be, and you can make some grave mistakes in the real world if you overestimate the normality of real world distribution. I recommend Taleb's works here, if you need more details.