So, getting back to the original topic, what is the "purpose of a black hole":
Can anything in nature actually be said to have a purpose? I submit that a purpose is like a sound. If there isn't anyone around to hear it, a tree does not make a sound when it falls. Someone's ear drums must be there to turn the pressure waves in the air into auditory impulses for our brains to interpret as sound. In order for a thing to have a purpose, something must be intended and something must be achieved.
An object may exist in and of itself with no effect upon its surroundings. It has no purpose.
An object may have some effect on another object, large or small, is this effect a purpose? No it is not.
So, a black hole has no purpose, unless some intelligence assigns that purpose. And if purpose must be assigned, there really isn't any purpose at all!
I suggest a better question is what does a black hole do?