very high temperatures - >40C - are, in themselves, life-threatening and need to be reduced.

As I always say, "life ain't binary". But the advice to the general idiot in the street, currently for COVID-19, is "to avoid ibuprofen and asprin", because they are vaso-dilatory.
If you are in hospital, it is a different context, you have the extended knowledge of experts, who have thermometers and are not afraid to wield them.

Some experts advocate Tylenol which would appear to be nothing more than Paracetamol which has been cited as not much better - and is also antipyretic BTW. Though is not anti-inflammatory which is a plus apparently.