This is a classic way to teach use of a sword. It's also easy to feel what happens. Compare the feeling when gripping with first two fingers vs 3rd and 4th. With first 2, you will feel tension along top of forearm, whereas with the other 2 it is the underneath of forearm. This affects flexibility, softness, and thus ability to manipulate the sword.
This tracks with my experience fencing using a pistol grip. The index finger mostly gets in the way and I even injured mine using it too much. The middle finger is the main driver of grip and control.
Similarly, holding a chef's knife you wrap your thumb and index around the blade, with the remaining three fingers around the handle:
https://www.epicurious.com/expert-advice/how-to-hold-a-knife...