Yes, I know, as I'm sure does Felsenstein. The book covered much more than maximum likelihood. The recommendation to report likelihood ratios came in the first of two chapters on Bayesian methods. The second involved hidden Markov models.

The book begins (as does the field) with a tree-building method called 'maximum parsimony'. Maximum likelihood is a step up in sophistication from that, and Felsenstein is largely responsible for that step forward. I'm not really sure why he is not an enthusiastic Bayesian. My guess would be that it is because he is a professional statistician and the whole discipline of statistics traditionally consists of ways of drawing totally objective conclusions from data.