Tier 3/4/5, namely for commando, is a good place to leave LMGs, instead of trying to shoehorn them into a full lineup to make another perk.
Players surely expect a little more out of LMGs than out of a basic assault rifle. Tier 2 is where a basic assault rifle fits into KF2's balance. So a tier 2 LMG would be a bit disappointing, while a tier 1 LMG would be hilariously disappointing. I'm imagining a M249 SAW burdening you by 10 weight, while the thing is only loaded with 20rd mags.
One of the potential gameplay mechanics that come to mind when thinking of machine guns is overheating, but to make that a part of a new LMG perk in KF2 would be kind of backwards. Half the point of an LMG is that it handles heat better than an assault rifle, and assault rifles already have zero issue with heat in KF2.