Reading the paper I think they used both SVDquartets (coalescence-based explicitly for ILS) and concatenation + maximum likelihood, which is a very sane combina

Reading the paper I think they used both SVDquartets (coalescence-based explicitly for ILS) and concatenation + maximum likelihood, which is a very sane combination for the analysis. Not contradicting you here, but at their scale it is unlikely any Bayesian approach will converge, so they had to settle with whatever they had to quantify uncertainty (branch supports and others). Edit: and also the Bayesian approaches might have model mismatch, for example I am not sure what's an accurate Bayesian method that models hybridization and ILS