The Mongols would disagree with you that its hard to shoot a moving target with pre-gunpowder weapons. Crossbows are ridiculously easy to fire at moving targets. You can definitely swing more times with a melee weapon. It can also be dodge, parried, blocked or absorbed much easier than a ranged shot. Melee attacks should not have additional effects besides damage unless it is due to a magical effect. Most monsters are melee based as has been pointed out in various posts in this thread. If you assign PC damage and effects you have to add it to the monsters and they have to be FAR more devastating! A giant striking you with his great sword or a gargantuan red dragon biting you would cause horrific damage. There is a reason that most monsters do not have an rider on their damage because it is not needed and would make combats too deadly.Ranged weapons should be hell a inaccurate against moving targets. Especially if you aren't taking your time to aim. I'm talking below 10% of the shots made finding their target at mid distances even if trained.
Also I'm sure you can make more stabs in a 6 second round that you can fire arrows.
In fact melee disparity with ranged should be so big that while safe. Playing ranged should be downright unfun in terms of effectiveness.
Melee attacks should be much more brutal when they land. And should have many more effects than mere HP.