Of course the age of consent is arbitrary. It has to be, because it has to be the same in all cases. If it wasn't, it'd have to be decided on a case by case basis, and how would you prove in a court of law that someone was or wasn't mentally mature enough to give meaningful consent to having sex? Plus, the behind prosecuting someone for statutory rape is that the adult is mentally mature enough to realize that they shouldn't have sex with someone who's mentally immature, which is why you don't prosecute two 15 year olds for statutory rape for having sex with each other. If you decided on a case by case basis, in the case of a very mentally mature 14 year old having sex with a mentally immature 16 year old would you have to prosecute the 14 year old for statutory rape? And... well, it'd just be a tangled nightmare to do it that way.