> I was extremely confused as to why the Normal (Gaussian) Distribution pops up everywhere—in kurtotically-ignorant financial market analysis, in nature, everywhere. Thinking about it, the prevalence of the Gaussian is actually rather abnormal. Can you guess why it’s everywhere?

This is not a "compression of data" question. It's not an "uninformed distributional choice" question.

It's a "why is this distribution prevalent in Nature" question.

In this context, I think the CLT gives a better answer. There are a lot of averaging processes in Nature, and due to the CLT, averaging of independent perturbations must give rise to normal distributions.

It's possible to perhaps go a step deeper than the above. In some physical systems, you can look at the second moment as an energy -- like the voltage-squared in electrical systems.

In this case, due to a-priori finiteness of system energy, the gaussian distribution can make a claim to being "inevitable" by the maxent argument in OP. ("In a system characterized by finite energy E, what is the least informative distributional constraint?")