What a funny coincidence. One S. Joshua @Swamidass is a co-author on this article from back in 2017:
Which says basically all the same things I’ve been saying, this time also supported by simulations:
Abstract
“Functional Information”—estimated from the mutual information of protein sequence alignments—has been proposed as a reliable way of estimating the number of proteins with a specified function and the consequent difficulty of evolving a new function. The fantastic rarity of functional proteins computed by this approach emboldens some to argue that evolution is impossible. Random searches, it seems, would have no hope of finding new functions. Here, we use simulations to demonstrate that sequence alignments are a poor estimate of functional information. The mutual information of sequence alignments fantastically underestimates of the true number of functional proteins. In addition to functional constraints, mutual information is also strongly influenced by a family’s history, mutational bias, and selection. Regardless, even if functional information could be reliably calculated, it tells us nothing about the difficulty of evolving new functions, because it does not estimate the distance between a new function and existing functions. Moreover, the pervasive observation of multifunctional proteins suggests that functions are actually very close to one another and abundant. Multifunctional proteins would be impossible if the FI argument against evolution were true.
[Mod edit to fix line formatting]