But the variance needs to be bounded. With power laws is is often unbounded. The trick that many get trapped in is that short samples of power laws typically look regular. Estimates of variance will always be finite on finite sample size. Nassim Taleb goes into more detail on this.

Then, Taleb is a jerk when someone tries to pin him on one of his wild exaggerations.

Even as a quant Taleb was prone to smushing over details to push a narrative. In the 90s already Derman was enabling Taleb into claiming the Black-Scholes formula was an interpolation algorithm already known to option traders and served basically to justify using the risk-free rate as a drift (price trend) parameter in accordance to the "economics establishment". But (as noted by more than one response in the literature) making a different assumption on the drift (or even the distribution) -- i.e. leaving the "Black-Scholes world" and merely interpolating two world-states -- you're left with calibrating a stochastic discount rate that gives put-call parity. But hey, not that technicalities should get in the way of a good story!