I feel like blunt damage would have made more sense for MCH.

[Anova]

I think the damage type is not to describe the actual physics of the attack but the type of damage being inflicted. Try thinking about it from the actual type of damage and nature of the wound you receive from it.

Bullets do the majority of their lethal damage by penetrating in to the body to attack something vital (like a lung or your heart). The slug then shatters in to somewhere from a couple to a dozen shards in the body to continue gouging up any surrounding organs and tissues.
It does pierce through armor because it is a blunt object, but the actual damage is caused by the round being stuck in your body turning your insides in to sausage.
When someone dies, it's usually because the bullet pierced the something like the stomach so the acid and metal shards are eating out your insides while they rush you to the emergency room; not because the bullet smashed the kneecap (blunt) or grazed an arm (slash).
By the way, this is the same thing that happens with arrows. Hunters don't have to poison them, they just pierce the body at a good point and track the beast for 10 minutes for the blood loss and gouging to do its work.

That's why it's piercing damage and not blunt. A fist or a hammer does not break apart to get stuck in your body to do the same sort of damage a bullet or arrow would.