There isn’t one, because we still don’t know how acetaminophen works.
Aspirin has been in use for thousands of years and what it does to the body was a mystery for 90% of that time. But no more: ibuprofen, diclofenac and other NSAIDs all use the same mechanism, inhibition of two enzymes that promote inflammation, cause platelets to be sticky, but also destroy your stomach lining. We tried to get cute and selectively inhibit only one of those enzymes because the other caused gastritis, but that didn’t go well. That part of the aspirin family tree was cut short. There is, however, a whole separate branch that builds on aspirin’s effect on platelets. The more we know the more we don’t know, and at the edges of our knowledge lie new drugs.
The acetaminophen family tree is a stump. On one hand this isn’t a surprise: we have only known about it for 150 or so years. But then pure aspirin was synthesized around the same time — it was just willow bark extract Acetaminophen was derived from coal tar so it is, in fact, coal tar extract. Somewhat off-putting for something to be taken by mouth, though coal tar can do wonders for dandruff. before the late 19th century — and look at how much we have learned since then. The best we have come up with is that acetaminophen works sort of the same way as aspirin, but only in “the central nervous system”. Vagueness covering for ignorance, like The cure? Heavy cream and butter. generic life “stress” causing stomach ulcers.
Our knowledge gaps are so large that we still can’t agree on the name. Is it acetaminophen (APAP for tired interns who hand-wrote their notes) or paracetamol? Or just Tylenol? More vagueness.
Which is to say, there can be no mechanistic arguments for APAP risks and benefits as we know nothing about the mechanism: all inferences must be made empirically. And our 150 years' worth of popping coal tar pills have shown them to be safe for everything but the liver.
Still, it is worth acknowledging that APAP is a molecule extracted from coal tar whose mechanism of action is unknown but has something to do with the central nervous system. If someone described such a drug and then asked whether it could be behind some disorders of the brain, would you find the question completely whackadoodle? I would not. And would in any case practice myself and recommend to my patients via negativa, whenever possible and sensible.
The number of ways in which one can spend money for biomedical science is infinite. America has sunk trillions into genetics research, with a few important wins to show for it but not nearly as many as hoped for in the early 2000s. For those too young to remember, this is the time when media were full of headlines about scientists finding the gene for x, where x was everything from hypertension to obesity to being gay. None of them panned out. Would a fraction of that being allocated to figuring out how one of the most widely-used drugs actually works be such a waste?