I think overruns were highly useful some versions ago, like 6.something. At that time it was difficult to hit dug-in infantry even when you were adjacent (actually you could do it rather easily by attacking the hex instead of the unit, but that's another story). By now it's probably more efficient just to shoot, unless you have low-caliber guns, but the coolness of overruns is still extremely high.
On the other hand, I never had much success with meleeing infantry, it's too difficult to get close compared to blasting away at range 1, which is safer because it's generally going to rout the squad anyway. One time there was a single enemy soldier left in a house, who had survived countless volleys of direct fire. I then entered the house and initiated melee combat, and he survived several attempts. Maybe he was hiding under the bed or something.