GM'ing Question: Carrying Guns and Encumbrance

[Raellus]

So, a few of my players want to carry more than one primary long arm (assault rifle/battle rifle/sniper rifle/LSW/SAW/GPMG, etc.) at a time. To me, this seems very unrealistic. I've seen literally tens of thousands of photos/videos of soldiers in wartime and I can count on two hands the number of times I've seen a soldier carrying more than one such weapon at a time and then only under special circumstances (carrying a wounded comrade's weapon for him, collecting captured weapons, showing off, carrying a breeching gun or small GL as well as an AR, etc.).

I get a sore shoulder carrying my slung Mossberg 500 for a mile hike.

Anyway, under game rules, players are well within their rights to carry multiple long arms as long as they don't go over their carried weight limit. I just don't buy it. I will allow PCs to carry a primary long arm and then another smaller weapon like an SMG, short-barrelled shotgun, or collapsed carbine (in addition to a sidearm as well).

I've instituted a house rule that PCs may carry multiple primaries but at a penalty to movement, innitiative, and to hit rolls.

Am I being a hardass? Am I the one being unrealistic? Is my stance reasonable? What do you think? How would you handle this issue as a GM?