One of my majors was Philosophy and I'm often disappointed by the attitudes of Feynman, Hawking, and other scientists towards philosophy. Their domain is science and I don't think that it is their place or right to judge the value of other disciplines as they apparently do not have a deep understanding of the subject.

Questions like "what is life" have serious implications for biology and arguing over definitions is important because it ensures that when we say something like "a virus is not alive" we have a well grounded and justified basis on which to make that claim. If we didn't take the time to argue over definitions we would have scientists arguing past one another because of trivial misunderstandings about the meaning of words rather than arguing over some other actual significant point such as the conclusion that can be drawn from the evidence. The role of Philosophy is often described as providing us a framework for reasoning.

Philosophy typically intersects with science at the "edges" where we are making novel discoveries in both disciplines and don't really know what to make of them yet so we have to reason about the evidence and concepts to make sense of it all so we can proceed.

You mention Physics, and the big debate in philosophy is whether the Standard Model describes reality as it is, or whether it simply a convenient tool where equation manages to encompass most of the empirical results we have so far. I'm not sure exactly where you are going with Bayesian methods but probability is definitely a focus of some philosophers and our department head wrote a somewhat influential paper about different concepts of probability. (a "taxonomy" of probability if you will but that might be a controversial way to put it in an academic setting just like the rest of this post)
Edit: I might also add that this professor had a Phd in philosophy as well as theoretical physics, so really smart guy, and the TA had one in physics and was pursuing one in philosophy, so also a really smart guy.

It's also important to note that philosophy of science by and large does not aim to judge the merits or validity of science/scientists/scientific theories. The point is more to understand "what is science" and provide a passive definition instead of a passive one if you will.

Philosophy of Mind is a "hot" branch right now as well and it remains to be seen if any significant progress will be made in the next several decades. We still don't have a consistent way to discuss "consciousness" and if you read literature coming from people with a computer science background, then from a psychological background, then a neurological one, you will find that they describe it in very different (and likely incompatible) ways.

I've forgotten the context specifically but there is a degree of controversy over the diagnosis of bipolar disorder and schizophrenia since the diagnosis rates vary wildly depending on geography even when patients display the same symptoms. The implication is that neither disease is "real" and is instead a result of the training of psychiatrists. Yet we still don't want to abandon the idea that these people are mentally ill so how do we provide a coherent definition of a mental illness. It seems to pertain to consciousness in some way and if so how? We can't answer this way with out a coherent and consistent way to discuss consciousness which we still don't have.

I hope that gives you a bit of insight even if this comment comes across as disjointed and I have been willingly vague and partially inaccurate at points because you could spend a lifetime reading on some of these subjects but still not consume all of the relevant literature. This again probably reflects the difficulty that you had with that book. Philosophy of Science is already a somewhat specific branch that is difficult to approach without some background in philosophy already. In a way that book is an introduction to a specific branch of philosophy that assumes a large amount of background knowledge.