I try to imagine self-defense scenarios.
In most cases I think I would do better with empty hands.
I think it would take something very threatening and ambiguous to make me put a knife in my hand; perhaps people acting in a belligerent manner but not quite stepping over the line.
In which case, would the knife push it over the edge into violence or would it have sufficient intimidation value to keep things from getting worse?
For me, in a self-defense situation, I might try to draw my Greco Persian in a point reversed grip, or Mexican carry, edge away from the body, and keep it out of sight along the seam of my trousers.
This might work better for me as a left hander than for a right hander.
In the Mexican carry, if someone tries to hit or push me with their right hand, my left hand will naturally come up to protect my face and neck, and without me really doing anything the aggressor will probably cut himself on my knife while in the act of trying to hit me.
However, that said, the point forward paintbrush grip gives the defender greater reach and IMHO more cuts per second delivered to the aggressor and more opportunity to puncture body cavities.
I can only think of three natural puncture movements with the knife in reverse grip: kidney, collar bone and cross body backhand; and I'll bet folks who have some training in the reverse grip can name some more.
Still, it seems to me the point forward lends itself to a greater variety of natural stabbing, or puncturing movements.
Recent reading, and 18 years as an EMS helicopter pilot, indicate to me that even a minor puncture of a body cavity, abdomen or thorax, quickly stops the fight; whereas I think some people can take a lot of superficial cuts before they realize all the blood has come from themselves.
In summation, then, the point reversed grip allows one to keep the knife hidden easier and lends itself, especially for the left hander, to defense by a natural response; raising the hands in a block.
The point forward paintbrush grip IMHO gives greater reach and more natural cutting and puncturing movements.
It would take an unusual set of circumstances to make me choose a knife over my hands, but it could happen.
For that reason, amongst others, I carry a self defense knife.