My kid is teething at the moment and he’s running like a faucet. What’s the purpose of drooling while teething? Is it supposed to serve as some sort of lubricant or something or is it just one of those things that happens for no reason?
I don’t have a medically based answer, just an experienced mom’s one 
I think they drool so much because it’s a reaction to the inflammation of the gums. Our youngest drooled the most of any of our children, and she was the earliest to cut teeth. I don’t know if there is a correlation between that or not, but it does seem that as they get older that they swallow more of the saliva rather than let it drool out of their mouths.
Like Adoptamom_ll, I have no medical expertise.
Look at it this way, the gums are irritated and sore. The saliva provides some sort of relief. It’s like having chapped lips and all you want to do is lick them. It doesn’t solve the problem (and maybe makes it worse) but it makes them feel better for a second.
Some day you will look back on that drooling baby with some of the fondest memories of your life.
I would think it’s just because it hurts (at least, isn’t comfortable) to close the mouth, not because there’s more saliva.