This is one of the results of running a completely synthetic Bitcoin.

I started with the a model distribution of the slopes (you can use a Lorentz or a t-Location Scale distribution) based on the observed parameters.

This is a time invariant distribution (it is the same distribution from the start of Bitcoin history).

Then we can derive the returns by multiplying by a deterministic factor (it is not random), log(t+1/t), representing the theoretical log returns from the power law, t is time from the Genesis Block.

You then compound the returns over time. This doesn't include the bubbles that should be modeled separately.

You can see we get the power law just from this distribution.