Given that the dominant infantry formation of the day was a tightly packed group of pikeman ( called a tercio in Spanish, I believe, that was almost viewed as unstoppable.) Throwing it rolling grenades, even from a short distance could disrupt a charge and bridge the gap created by the long pikes of the day. Especially in an era of single shot slow reloading muskets and artillery. Grenadiers were typically recruited for size and strength and were viewed as shock assault troops much in the same way Eastern Euro armies have “Guards” divisions.

But this is really more a 17/18th century usage. 14th C the English longbow and German short pike were the battlefield weapons of choice.