Those "endless" arguments you speak of are actually something I consider to be one of the strengths of philosophy! In engaging in philosophy, you don't stop at the assumptions, you questions the axioms themselves. What is the context that produced the certainty of the axioms? Do they hold from all perspectives.
Although there is always a sense of potential circuitousness to philosophical discussion, and a sense that there IS IN FACT NO FINAL(/CORRECT) ANSWER, this can in fact be what's considered the strength of philosophy - that it shows how infinitely mysterious life is! I consider this to be the fun that is philosophy, but of course it's not everyone's cup of tea
Given the utter bilge that philosophers have seriously propounded, and the endless arguments with no resolution between different schools of philosophy, I'm not sold on their "meticulous method" having much to offer to physics. I mean, yes, at it's best, philosophy has something to teach physics about meticulous though. But at it's best, physics already knows it.