Long discussion that took many years to resolve.
MP doesn't account for back mutation, which is a HUGE problem for nucleotide data because in theory 1:4 mutations is a back mutation. Maximum likelihood has resumed is crown here, however Beast deployment of a Bayesian calculation is also very widely, particularly for molecular dating. ML uses a reversible matrix A <-> T, whilst Beast uses a directional matrix A->T and will score T->A separately.
Happy to discuss the approaches and modern interpretations at length.
The model which accounts for back-mutation is the Jukes-Cantor correction (JC correction), this is a basic model present in every phylogenetic algorithm except p-distances). Essentially JC extrapolates back-calculation for the true number of mutations against the observed number of mutations against divergence time. However, when the P-distance (uncorrected observed distance) exceeds 0.75 for nucleotides the model is not viable. Basically, nucleotide divergence >0.75 is saturated and the phylogenetic information is essentially random.