Licking an actual wound might be advantageous. (But maybe don’t do it just yet.)
There’s all sorts of stuff in saliva. Caterpillars can produce silk with their salivary glands! Snakes have venomous saliva they can inject with fangs! People aren’t as exciting, our saliva’s got minerals, digestive enzymes, microorganisms, antibodies and proteins. One of these proteins, histatin-1, has been shown to expedite wound healing. This protein is capable of promoting angiogenesis, which is the creation of new blood vessels. Those blood vessels deliver all sorts of nutrients and oxygen which will speed healing along. Histatin-1 also plays a part in cell migration and adhesion (it gets the new cells in the wound to stick together). Wounds in the mouth heal fast. The salivary protein may be a major reason why. In the future, we might be able to put this protein into other bodily wounds to speed healing along. FUN SALIVA FACT: you produce about a quart of saliva per day, about the same amount as 2 standard bottles of water. That’s a lot of saliva.
To read more about your saliva’s wound healing capabilities: https://www.sciencedaily.com/releases/2017/08/170807110331.htm