Reducing fevers is a mixed bag. Yes, the higher temperature may help fight the disease (or might do nothing, totally dependent on the diseases suitability for reproduction at higher temperature). Yes, it can also damage your body if it gets out of control. And yes, sleep is also good for fighting off illness, and a fever can get in the way of that. Just because it is your bodies natural response doesn’t mean it’s going to help you. Allergies are a great example of the body taking totally inappropriate counter-measures.
True, but cases of fever harming the body are extremely rare. The fact that mammals, reptiles, and even insects, increase their body temperature to fight pathogens suggests that fever confers significant survival advantage and that our null hypothesis should always be that it is helping us unless we have strong evidence to the contrary. I agree that sometimes (rarely) our immune system does get it wrong in a serious way such that medication is crucial (for example, anaphylaxis); however, most immune system misfires are minor and do not justify the risk of medications with poorly understood side effects and interactions. Oftentimes, there is a good alternative to medication. For example, when I have sinus congestion, I can almost always find a head orientation that allows me to breath and sleep.