This one tests something that I have been tempted to call a deliberately constructed strawman of evolution.
Axe and Gauger take two distantly related proteins that share a common ancestor billions of years ago, then they pick some amino acids from extant protein A and replaces the amino acids at corresponding positions in extant protein B, and observe that following this protocol, they are unable to convert A directly into B without losing the function of A before they get to function B.
This is sort of analogous to taking a pig and then seeing if you can directly convert it into a squid by picking mutations from the Nautilus genome and inserting it into the pig genome and then producing a dead organism.
This is of course not actually a test of any evolutionary postulate, as both pigs and squids evolved from a common ancestor, they did not evolve directly from each other, and evolution is not contingent on the reality of some sort of pig-squid hybrid being able to live.
That’s the same trouble with this paper, it ignores the common ancestor and instead tries to do a direct conversion of one into the other.
A proper test would have been to use a phylogenetic algorithm, try to get a lot of diversity of proteins from the same family, and infer the evolutionary phylogeny of these proteins, then reconstruct ancestral nodes and recreate them in the laboratory to test if and how they work, to get an estimate of the history of mutational changes that gave rise to these two proteins from their common ancestor.
For mysterious reasons Gauger and Axe didn’t do this and opted instead for their weird direct conversion scenario that nobody says or believes ever happened.