It's definitely necessary for some people. I'm allergic to NSAIDs, though to differing degrees. Really bad hives (to the point of needing epinephrine) from aspirin, less severe reaction to naproxen.

I can tolerate a single pill of ibuprofen, maybe 2 in 24 hours but that's it. I don't take acetaminophen frequently, but it is one of the only things I can tolerate for pain (sinus/tension headaches mostly).