IMO, this sounds like a promising alternative to conventional phylogenetics. However, I think the methodology will need an upgrade to be really useful, unless the purpose is limited to obtaining a crude phylogeny rapidly.

It seems like the method suffers from the same principal drawback as a conventional multigene analysis where genes are concatenated: the outcome is a phylogeny where species distances are based on average coalescence, which results in exaggerated tip branch lengths. This outcome is actually discussed, but only as a method artifact and not as an expected consequence of population genetics. If I understood correctly the evolutionary distance (d) is a point estimate of average coalescence. But without a coalescence distribution it is impossible to accurately estimate speciation time.

I like the concept of basing a phylogeny on pairwise distances, because it permits to test whether the species phylogeny is a tree or a network (owing to hybridisation). However, the method as presented does not explore this and naïvely assumes that the phylogeny is a tree. But most people do this anyway regardless of method.

Finally, how can this type of data be used to produce a dated phylogeny? It is somewhat inconsistent that the produced phylogeny is a phylogram, based on genetic distance, while the coalescence process that distorts the tip branch lengths operates in time.

"Normal" phylogenetic methods performs well in most cases, with limitations. Kmers-based methods can produce good trees with a few mammals species, but what happens if they are used with hundreds of bacteria? I am afraid distances would become rapidly uninformative. Maybe it can be ok for mammals, but for deep phylogenetic trees, no way, maximum likelihood phylogenetic reconstructions, and accurate selection of the genes to input remains the best we have in hands. The selection is not a limit, guided by additional informations it is instead a resource because gene phylogenesis is often different from species phylogenesis, but there are genes that are less easily transferred and that can provide insights into the correct evolutionary relationships among the species. One may select slowly evolving genes when building phylogenetic trees with distant species, or rapidly evolving ones when the species are very close.