Given it seems ALL young kids have this nose-wiping aversion across cultures and racial ethnicities, it would seem that this reflex reaction is hard-wired into human babies. But why would evolution favor this reaction?
I tried to find an answer to this question to see if any bright researchers actually studied this topic, but was unable to find any. So... here are my thoughts on this topic.
To warn other healthy humans
Evolutionarily, it may have been helpful for the human population as a whole if it was obvious to others when an individual was sick. To see a toddler with snot running out the nose, that would have been a pretty clear sign for other children and their parents to stay away lest they also get sick. This isolation of a sick child would have been nature's way of quarantining to prevent spread of illness to the rest of the human group.
To get eaten by predators
Not to be morbid, but predators tend to feed on the sick. It is nature's cruel way of removing the weakest in an animal population which over time will only strengthen the prey animal population as a whole (Darwin's theory of only the fittest survive). Back in the REALLY old days (caveman era), sick humans would have been just such a prey that would have been targeted by wild predator animals. To be not just a young human, but one that also shows signs of illness would be indicators to a predator of who to go after.
Protect the airway
This is my wife's favorite theory who feels the last idea to be horrible and inhuman (never mind that just because evolution is horrible and inhuman does not make it false). This airway idea is based on the fact that breathing is essential to life. Anything that covers the nose or mouth, even briefly, is a potential hazard that may lead to death. Evolutionarily, this reflex would be favored and strengthened over time... even if avoidance involves just a quick wipe. Who knows? Perhaps SIDS (Sudden Infant Death Syndrome) would be much more prevalent if the nose/face wipe aversion was not present.
Any other ideas? Even better, does anybody know of any studies that actually looked into this topic?