That's not true, though – substantive inquiry is certainly not just a conversation. Philosophy puts on some of the superficial trappings of inquiry, which involves discussion, but if you look closer, often no inquiry is happening. — Snakes Alive
The process of actually doing the inquiry involves a lot of stuff that is not just conversation, yes, but the process of setting up that process is very much like talking about talking. To get something like science underway, the people involved need to have broad agreement on some general things, like:
What do the questions we're asking even mean? What exactly are we asking, in this inquiry? An answer to this could be something like the verificationist theory of meaning. Analytic philosophy leans very heavily on this kind of question, and arguably even the Socratic dialogues are basically quests for adequate definitions of the terms used in other, more substantive inquiries.
What criteria do we judge answers to those questions by? What counts as evidence that a proposed answer to a question is true? An answer to this could be something like empiricism.
What method do we use to apply those criteria? An answer to this could be something like critical rationalism. This is the part most like the "litigation" you're emphasizing, having to do with burdens of proof and such. Is some account of the world to be presumed right by default until we find some reason to think otherwise, or are no accounts acceptable until one has been conclusively proven, or are all accounts equally possible until we find some reason to judge one over another...?
What should we take to be the relationship between the objects of our inquiry and we, the subjects doing the inquiring? Are we to think ourselves objective judges of something wholly independent of us? Or that the objects of our inquiry are dependent upon we subjects, created by us or by the very act of inquiry? Or that we subjects and the objects of our inquiry are interdependent parts of one system and what we're actually investigating is the relationship between ourselves and other things no different than us?
Who gets to do this inquiring? Is this to be a decentralized democratic process, or do some people have privileged or authoritative positions and their judgements carry more weight than those of others? Does it matter how many people make the same judgement? How, generally, should the social endeavor of inquiry be organized, for its findings to be reliably legitimate?
What are we asking for? Why are we inquiring into the things we're inquiring into? What is our objective or purpose? What use are answers?
These are the kinds of questions that philosophy purports (and I argue, genuinely endeavors) to answer.