Thus, every pregnant woman prayed for a boy, who would fulfill that prediction and each new baby boy was named Samuel. Your frustration, if I understand it correctly, is that this explanation may be satisfactory insofar as it pertains to Chana, but it still leaves unresolved the question of why so many women throughout Jewish history have specified male offspring in their prayerful requests. Based on this question I am compelled to go further, in an attempt to offer you a deeper response. The reality is that Hashem did in fact give men a greater number of mitzvot. Our sages tell us that men enter the world less spiritually complete than women and, for this reason, they have been given quantitatively more commandments with which to grow.
Women come into the world spiritually more complete than men.
They have less to accomplish in this regard and, therefore, they have fewer mitzvot. Being that we aspire to have as many opportunities as possible to serve God, a woman might pray for a son who would come into the world with the longest possible list of commandments with which to serve his Creator. If we go a step further, however, we realize that the playing field is more level than it might seem. First, despite the fact that a man has more mitzvot, neither man nor woman is able to complete his or her list of duties in this world. Therefore, it would be a mistake to take a list of potential opportunities and use them as a basis for actual spiritual accomplishment.