Covenant weapons tend to be more useful than UNSC weapons, for instance. Plasma Repeaters don't need reloading, only periodic cooling. And the Needle Rifle's ammo explodes when shot into an unshielded target, again proving my point. Ghosts are better at splattering and don't need an extra gunner. UNSC Troopers know this from experience and probably instituted the training programs themselves. SPARTANs and ODSTs obviously are fluent in Covie weaponry as well.
And what if they're out of ammo after they killed a Covenant squad, but there weren't any crashed Pellies Albatrosses nearbry? First Instinct: Get a plasma weapon off the ground!