That sounds to me like they were using a coalescent model within a single population. In that case, the topology and node heights of the gene trees might be regarded as nuisance parameters to be integrated out, with the real interest being the population parameters. But you read the paper, I didn’t.
They were actually interested in clade posterior probabilities.
I’ve had very good luck with very short conserved intron sequences (e.g. 46 informative sites) for rather deep splits in cone snails exactly because the “fingerprint on the pipe” was so clear. The absence of conflicting sites made the phylogenetic signal super clear. So clear that my habit of using Spectral Splits was a formality.
I’d like to find many more of these sequences. Such seems to be the best case for very deep splits such as at the base of the eutherian tree with a comparable tree depth. Any ideas on looking not for extraordinarily long noisy sequences but for short sweet ones?
Its probably not really a useful point, but the question of whether a polytomy is ‘real’ or not seems to me to depend on how you view ‘what’ the the phylogeny is representing. I can imagine a case where there were two sequential bifurcations in a population of bacteria and the substitution rate is so low that in fact between the first and the second, there were NO fixed changes. In this case, the phylogeny of the populations would in fact be dichotomous, but the phylogeny of the genomes is polytomous.