I'm pretty sure wealth doesn't follow an exponential distribution. Power law, log normal or stretched exponential or maybe some sort of generalized Zipf.

This, for the sake of argument, is not an important distinction.

I disagree, if anything we need to know what the distribution is before we make such sweeping claims. While pretty much every country has an income tax, which means that we knows fairly well who makes what, there is no equivalent for wealth. Most wealth distributions are estimates which get progressively worse as we near the top percentiles, because really big wealth is very mobile and international.

So yeah before we say: "it always looks like this, it's just about what the parameters are", we need to measure it and have a clearer idea of what it looks like in different societies otherwise we won't be able to decide what the desirable parameters are like.

Don’t use technical terms like “exponential distribution” and then say the technical details like what distribution it is does not matter.

Doing so conveys sloppy thinking while pretending to be rigorous only on the surface.

Why is there an always an exponential distribution of wealth?

Just because there is a power law relationship doesn't justify having such a steep curve. Flatten the curve, the rich should pay more tax.

The alternative is returning to a feudal gilded age where there are a very very small cabal of asset owning lords, a very small class of scribes for the lords, and then a sea of serfs.

You make it sound like some kind of natural law that we have no saying over. It isn't.

The whole concept of wealth accumulation is entirely human-made, and influenced by what the society is willing to tolerate.