It does matter what the actual active ingredients of medication are, even in pain medication, whether the general population cares about that or not. These things really do have different properties and side effects, pain meds are not interchangeable.
But that shouldn't distract from your general point which I find hard to disagree with: pain medication is symptomatic relief. That doesn't make it irrelevant, but it doesn't mean people should ignore the underlying causes either. At the same time, these causes are sometimes idiopathic, (short term) unavoidable or (long term) untreatable.