Even at secret squirrel levels, a mission brief would include a specified ammunition load. Guys might scrounge up more, but even if you're on SEAL Team 6 if you show up for a raid with a two M4 and two pistol mags because you don't think you'll need it or similar, people senior to you are going to start reconsidering your elite status pretty quickly.
Too much ammo is a different problem -- most game mechanics don't do encumbrance very well and encourage guys to parse out their equipment load to the microgram to meet a specific encumbrance load. You could maybe work some sort of fatigue rules or modify encumbrance rules (not familiar with the core game system in question) to be more nuanced and discourage guys from carrying quadruple basic loads because they have a high strength or endurance, etc.
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