Mechanically speaking, there are actually some solid reasons the middle finger makes sense as the preferred trigger finger, chief among them being a) the middle finger is usually stronger than the index finger and b) the tendon arrangement in the middle finger typically entails less rotation/torque as the finger flexes, usually resulting in a straighter bend when the finger flexes to pull something. Taken together, these things mean a cleaner, more accurate pull of the trigger with a stronger finger.
However, the above analysis (of the middle finger being used as a trigger finger) is in a vacuum, whereas trigger pulls take place not in a vacuum, but in the context of a hand that is also gripping and being used to assist in aiming. Once that context is applied, it becomes clear that use of the middle finger to pull the trigger entails tradeoffs.
The tradeoff one makes to use the stronger middle finger to pull the trigger … is a weaker grip due to the middle finger's strength no longer being applied to the grip. Worse, the (now useless) index finger can't assist with grip, resulting NOT in replacement of a stronger gripping finger with a weaker one … but instead in the complete loss of one (perfectly good) gripping finger on the pistol's grip.
Most instructors will tell you that grip+trigger control are two key elements of good pistol shooting. Which of these two elements is the more important tends to be a matter of who you ask. From my point of view regarding what's going on with the hand during a pistol shot, one's grip sets up the the foundation for the shot while one's trigger control serves as the mortar. You ultimately need both, but if I had to call one more important than the other, I'd say the grip/foundation carries more weight (to extend the analogy just a little farther

).
Thus, I see no viable reason for someone with four perfectly good fingers and one perfectly good thumb (on a single hand) to only use two of those fingers (instead of three) to grip a pistol. Similarly I see no good reason for someone to use the index finger for nothing … or to use it only to point. (Reminder: People have eyes … and pistols have sights for a reason ... so use them!)
Surreal
P.S. I deliberately left the support hand out of the equation just to keep things simple. Bringing the support hand into the equation doesn't change my perspective on the topic in the slightest.