Chasefox, that might be the case, since both Zelda and Link have been able to use Light Arrows.
Was playing through Master Quest a couple days ago, at the part where Link first meets Princess Zelda as a kid. If you'll remember the whole conversation they had, where Zelda told link of her prophetic dream, etc., Zelda tells Link that the reason no one (including the King) suspected Ganondorf was up to no good when he first came to Hyrule, was because the kingdom had just spent several decades of peace.
Furthermore, remember in OoT when the newborn Deku tree tells Link about the old war that ravaged Hyrule? Surely a lot of Hylians were killed in that war.
So, there are three possibilities I can think of as to why Hyrule's soldiers do not wield Light Arrows: it might be exclusive to those who bear a piece of the Triforce (as Chasefox suggested), Hyrule might have been disarming itself because of the seemingly peaceful time, and/or most of Hyrule's skilled fighters, or at least any mentors who could instruct in the art of combat, were dead.
Still, it would have been really cool to have a bunch of elite Light Arrow marksmen. Maybe in the next Zelda...