I'm completely guessing here, but I think the idea of giving average pilots a Piloting of 5 is that it gets the right amount of skill checks per game. Falling can really hurt you in a tight game, not just from armor lost but also from the sudden decrease in mobility. You can't jump the next turn, and you've got to spend 2 MP to get up. For some mechs that's a big loss. If the average piloting skill was a 4 or a 3, then falling would be rare enough that you don't really have to worry about it. If it was a 6 or more, then it would happen so often that it would be annoying, and could bog the game down.
From an in-universe perspective, having to make a piloting skill roll means you either took a lot of damage, or you tried to do something stupid. Turning while running on pavement requires a roll because you're trying to make a really sharp turn. Presumably you're trying to stay on the road, and you're taking a corner too fast. A smart mechwarrior would try to avoid those situations as much as possible. You're pushing the limits of your machine's agility when you do something that requires a piloting roll.