My “fever” and your “fever” might not be the same things.
I don’t get excited until it’s over 38 degrees celsius (100.4 F). At that point I’ll take blood cultures and worry about you. Anything under that level gets paracetamol (acteominophen) only.
If you’re afebrile and you took antipyretics recently, well, good for you, they’re working and you aren’t that sick.
If your temp is mildly elevated (say 37.6) and you took antipyretics, I’ll just make sure you get some more when you’re due them and keep an eye on you.
If you’re really sick, no anti-pyretic in the world is going to get your temp down to normal. If it’s over 38 degrees C and you’ve taken an antipyretic…I’m more worried than if you hadn’t, but I don’t do anything differently.
If it’s over 38 degrees C and you haven’t taken an antipyretic, you get blood cultures, I worry about you and you’ll also get an antipyretic.
Usually they don’t ask because it doesn’t matter… your temp is high, you get blood cultures and an anti-pyretic, it isn’t, you don’t. If you’ve taken an antipyretic more than 4 hours ago, it doesn’t matter anyway.
Temps under 38 are not going to do you any harm, you’ll probably get a fan and a cool washcloth, but not too much else in the way of specific treatment for the fever itself if you’ve already had your antipyretic.
Paracetamol is only of the weakest painkillers, most hospital inpatients are written up for it QID for pain, if they’re still spiking temps with that, they’re not going home, even if the pain is controlled. Fevers are signs of infection (usually).
Whether that is a bacterial infection, requiring antibiotics, or a viral infection, requiring supportive treatment only, has nothing to do with how high your fever is, and everything to do with how sick you are and the source of the infection.