You are indeed correct, yet differences such as these aren't really taken up by some in the population. A few years ago, if I was in throbbing pain, walking through the pharmacy, I wouldn't really have the time or energy (which is really bad and not thoughtful) to search the back labels or ask a pharmacist on whether I should be taking Ibuprofen or Acetaminophen or a placebo.
The point I was trying (maybe failing) to get at, was these drugs regardless of their chemical makeup, most of the time, some of us don't need them but we take the clutch anyway.
They are pain reliefs, not solutions to whatever the pain was caused by.
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.