Again, spears have very strong niche uses. They're never going to be, and should not be, as strong as swords or axes at infantry combat. Just as swords and axes are never going to be as strong as spears against cav or used by cav.
This is terrible logic. On the battlefield the spear is king, it is better than swords or axes against infantry. Swords are niche secondary weapons used in other situations, like when you lose your spear, when indoors, in a city, etc.
One on one unarmored duel wise, sword+shield is superior to spear+shield, but sword without shield is worse than spear without shield.
Your balance shouldn't come from cav>sword inf>spear inf>cav. It should come from other sources, such as tactics, formations, positioning, etc.