As I have posted in this thread before, the idea that hipfire stance is somehow tiring or seriously restricts mobility is incorrect.
The weapon is still putting 26lbs of weight onto the sling which is on your shoulder. Which way the barrel is pointing is completely irrelevant.
The only way to get some rest is to put the gun down or put it across your back, which is obviously retarded in a close combat situation.
Also, nothing prevents you from jogging or even running at a good speed and pointing the weapon forward. You'd have a hard time aiming and controlling the recoil though.
Best wishes,
Daniel.
The sling doesn't change anything significant, for several simple reasons.
The sling certainly lightens the load, but you still have to have your left arm extended and keeping the barrel raised at minimum. You also have to push the weapon forward so that you can reach the grip comfortably without having to reach behind your back to pull the trigger.
Next,
THE SLING IS ATTACHED TO THE UNDERSIDE OF THE BARREL AND THE UNDERSIDE OF THE PISTOL GRIP. See image below. Rely on the sling alone, and the weapon will roll upside-down. You need to exert an opposing force to the torque exerted by the weapon's center of mass and the tension force of the sling to prevent the weapon from flipping.
And if you want to control any sort of recoil, you better have a correspondingly better grip on the weapon. The sling alone will NOT help with recoil control, that I assure you, and your shoulder is not there to absorb the shock.

You will need to exert more effort to actually be ready to fire.
Finally, leaving the weapon to rest on your shoulder during hipfiring is suicidal if you need to swing the weapon around at all. If your life depends on trying to make a 90-degree turn around a corner and spray down a hallway, any soldier with half a brain will pick up the weapon's weight with both arms and exert every bit of necessary force to swing that weapon around. It's elementary rotational dynamics. It will turn faster if you put more force behind it. You can put more force behind it with your two hands.
In close quarters combat, you WILL be holding the majority of the weapon's weight to make sure you can maneuver it quickly and control the weapon's path so it doesn't clip the doorframe on the way out.
Look closely at that picture Sarkis linked. The soldier is holding a good part of the weapon's weight. (He would also need to worry about burning his left hand).
Do I also have to mention that you have to take the sling off to deploy the weapon properly? All the more reason for an iron-sight keybound hipfire mode.
So sure, if you're lazy, you could let the entire weapon's weight sit on your shoulder sling and blaze away while holding the pistol grip daintily with your right hand while eating a sandwich with the left. You won't hit a thing, the weapon will flip itself over, and if a Russian appears on your left, you'll be dead before you can awkwardly turn the weapon around to bring it to bear.
Cheers,
Nikita.
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Slow walk only. Iron-sights button-press to enter/exit hipfire stance please. That's all I have to say.