A zeroth-order argument for the utility of modern painkillers: you can take acetaminophen and ibuprofen at the same time for "twice" the effect, without either risking deadly liver poisoning from acetaminophen overdose, or stressing out the stomach lining from high-dosage ibuprofen or aspirin.

Those of us who occasionally get migraines know all about this, as do people in palliative care.