Having done historical shieldwall reenactment, you're wrong. Firstly, most of the representations are of spears far too long to be thrown, and in periods where this wasn't really common practice regardless.
Secondly, the overhand grip allows for a level change, now while your fellow spearmen stab at the legs and feet of the enemy, you stab over and into their neck/face. There is plenty of leverage to kill someone, and you actually have more of an arc infront of you where the spear is dangerous with an overhand grip. You'll also need an overhand grip to effectively fight 2nd rank with kite shields, the tail of the shield of the man infront of and to your right will severely restrict your movements.
A spear can kill you through chainmail, a spear can kill you through plate armor even. Chainmail primarily stops slashing blows, and makes you a harder target to hit square, as you will glance off at bad angles even with a spear, but a direct hit will penetrate and potentially kill. The gambeson may save you from a spear if it's very thick and paired with chainmail to allow less of the spear to reach your body as fast, but spearheads are plenty long enough (usually, there are of course exceptions) to reach through these defenses with enough force to kill you.
For an example in Bannerlord, look at the Thin Fine Steel Hewing Spear. That could reach through and out your back, regardless of the armor.