Then you should note that no army fields full-auto rifles - this too is a substantial difference between a modern AR and a WW2 SMG.
The Austeyr used by Australia (and New Zealand) has full-auto capability, as do most AK assault rifles. I’m pretty sure the M4 can go full-auto as well. They have rates of fire so high you’d be borderline crazy to do so in most situations, but in certain situations it’s a good option.
Exactly. But it is intended for the same purpose, to reduce recoil, allowing better rate of fire, sacrificing the performance at long range, or in some cases, just to reduce the weight. 5.56 round is a large upgrade over pistol round.
Obviously modern rifles are not full successors of WW2 SMG, but to say that armies moved away from SMGs is rather not true. If anything, armies mover away from WW1-WW2 rifles to a less powerful but more rapid-firing weapon, with WW1-WW2 style rifles only staying in the niche of sniper weapon.
Except performance at longer range hasn’t been sacrificed

. Modern ARs still provide the same things rifles did in WW2, and that’s still their main purpose. The M4 Carbine and M16 have longer effective ranges (500m and 600m respectively) than the M1 Garand did. Most SMGs then and now have effective ranges of 200m or less. You would not outfit a modern infantry unit with SMGs today, and you wouldn’t do it in WW2 either unless their primary business was relatively close-quarters combat (clearing out bunkers/high density urban warfare/jungle warfare/etc

. I’m not sure what other militaries are trained to do, but the Australian Army uses its assault rifles primarily in the same role (long-distance, single-shot – although semi-auto, not bolt action!) that rifles were used for in WW2. Most automatic fire is done by the LMG team in the section (again, similar to WW2, potentially with the Stg-44 aside).
As for the level of power, while an M16 and M4 use smaller rounds, they also have higher muzzle velocities (M16 moreso than M4, but both are higher than the M1) which offset, to a degree, the smaller mass of the round. The momentum of the round (and the formula I think Klausewitz was looking for earlier) is:
P (momentum) = m (mass) x v (velocity). Modern western assault rifles have lower m but higher v.
Most firefights happen at ranges not to exceed 200 m. SMGs were developed to provide maximum firepower at the ranges of the infantry rush into enemy trenches.
From my understanding, it varies markedly by environment. Many encounters in Vietnam in the Jungle were very close range – out in the paddy fields though not so much. Desert warfare tends to be particularly long range, urban warfare tends towards closer a lot of the time but longer in some cases depending on the layout of the area being contested. I’d expect much of the shooting on the Eastern Front, in open steppe country, to have been over a 300-400m distance or more. The versatility of the modern assault rifle (and modern carbines even more so) is that they can handle the long and short encounters well. SMGs now and in WW2 weren’t much chop if the engagement range was long (200m plus) which happened plenty.
Veering back on topic, the AK-47 has an effective range of 350m, and the Stg-44 of 400m or more (sources vary, the German army handbook claimed it was effective up to 650 yards), so it would be possible to produce these kind of proto-modern assault rifles in the period HoI4 covers, and I’d think that they would provide an advantage in firepower that, if provided to enough infantry, would warrant a small combat bonus. I still don’t think the difference between bolt action and semi-auto was significant at the level of HoI though.