Honkin’ big paradox ping.
The only reason that Neanderthal men had big noses is that Neanderthal women like ‘em big, and that’s the way they bred ‘em.
There seems to be an assumption that evolution is directed toward improvement. To the extent it happens it might be devolution, making something worse. Maybe a big nose was a failure. Where are the Neanderthal now?
Perhaps they lived at a time when it was warm, continental ice sheets came sliding down from the north, and they, and their noses, did not survive.