The spear and the pike did not disappear per se, it was just the gradual use of a normal spear (something along the lines of a hoplite spear - hoplon) instead of a very long sarissa pike that would have required consistent training beforehand.
After the Komnenoi dynasty, so essentially around 1190, the central Byzantine authority collapsed as well but it was not replaced by small, powerful states. It was replaced by other empires.Edit: Obviously the Byzantine empire did not suffer a similar collapse of central authority. However, they often didn't have enough soldiers to meet their enemies on equal terms, and so depended on maneuver to cut off the enemy from supplies and reinforcements. A slow, cumbersome army would not be useful.
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