> What is there to be gained by holding solder metal in the mouth?

Unless you have a third arm or a monkey tail, holding the solder in your mouth is about your only option when the component is in one hand and the iron is in the other.

If you spend any kind of time doing this you should just invest in a jig to hold the work. And solder is thin and flexible, it's pretty easy with a bit of practice to manipulate it with the other fingers.

Wiggling the joint while it's setting is sub-optimal.

Of course. But not everything fits into a jig.