Some people do find it virtuous to suffer a little, but that's another matter.
The “symptom” is an immune system response to a pathogen.
To me, it seems rational to default to assuming the symptom has an evolved purpose, a mechanism in fighting infection, and not counteract it unless absolutely necessary.
E.g. quick random Google: https://bmjopenrespres.bmj.com/content/3/1/e000118
"The commonest form of cough is caused by upper respiratory tract infection and has no benefit to the host. The virus hijacks this natural defence mechanism in order to propagate itself through the population."
He knew a lot about being ill.
A little less anecdotally, a cold is a viral infection, so medicine will mostly target only its symptoms, not the underlying cause. If the symptoms are bearable, then this looks like a bad idea to me - I'm inclined to think the symptoms are there for a reason.
The rest just makes you feel a little less awful. All the studies show the current OTC remedies don’t shorten illness duration (which conversely means they don’t lengthen it either).
The “evolutionary response” hypothesis is a lesser form of “smart people going with their gut instead of science” - which is partly how we’ve gotten into this mess in the first place.
Smart people seem to get important things wrong quite a lot.
Being unable to breathe through your nose serves little purpose I can think of.
Your 'most of Europe' doesn't really fit with my experience of the UK.
As a generally healthy Dane, when I get the cold or the flu I generally don't take any medications for it, and neither does most of the people I know.