Two turns to reach and get in the Falcon. One turn to get into the gunner seat. One turn to deal with bracing, activating the controls, turning them on, rotating to aim, etc.

They are on the ground. Now, that gunner position might be a formidable position in the air. But on the ground? (Scene of Mollari pressing a button as Morden yells "No!")

As soon as he manages to start shooting, it will be time for the other side (PIE fighters) to shoot back. And they will have the advantage of already having had a turn or two to aim/prepare - our side is "sitting ducks", they have all these bonuses to hit, and there is no way to get a bonus to defense!

Have you ever noticed all the ways, in most gaming systems, to get attack or damage bonuses, and the relative lack of ways to get bonuses to avoid being hit? Armor class goes up generally slowly. Hit points go up level by level. Spells to reduce the amount of damage you take? Sure. Spells to improve your armor class? Few and far between, and again, it's generally a single bonus that does not scale with the enemy's improved ability to hit.

Finn could be the best gunner in the First Order. He might have perfect firing, taking out one PIE per turn. It's still anywhere from one to three shots that hit them depending on initiative. More if he doesn't take them out in one hit. And if he can take them out in one hit—remember, these are newer PIEs, that are bigger and better defended, more HP—then what kind of damage will their hits do to the Falcon?

You want to take a decades-old rust bucket that was never working right, have it take at least two shots (remember, Finn and the Falcon might not be able to do one shot, one kill) from skilled pilots, and somehow still work afterwards?

That would take a miracle. And I don't see Miracle Max or a giant chocolate covered pill.