A single draw is a wild card. The average of a handful of them is a tamed one — and average enough handfuls, from any source at all, and the same bell appears.
The left lane draws from a flat uniform, the middle from a hard-skewed exponential, the right from a split bimodal. Nothing about these shapes is bell-like. Set the sample size to one and each histogram simply wears its source's face.
Instead of plotting single draws, each lane draws a small sample of n, keeps only its mean, and pours that one number into the histogram. Raise n and the skew and the split both dissolve — the averages forget where they came from.
The amber overlay is identical in all three lanes: a Normal with the same centre and a width that shrinks like 1/√n. Chance, piled deep enough, stops being chaotic and becomes iron law. That is the Central Limit Theorem.