The other side of the debate insists it's a measure of complexity a.k.a. cognitive load. This story amounts to an argument in favor of that.

I've been thinking of complexity as just a useful proxy to arrive at a decent estimate of time. But if "cognitive load is what matter" it's more than a proxy, it's the thing we should be estimating and focusing on.

Since the risk of mis-measured time increases as complexity increases, maybe it is indeed better to make story points a measure of cognitive load rather than just time, since the former includes a better way to estimate the accuracy of the estimate.