As much as I like your scatter data sheet,the issue here is that the barrage of the heavy mortar is very useless.
The time between shots is so long that you can only use it on structures. If you use it on enemy infantry, your opponent has plenty of time to move away after the first shot. Even team weapons can be moved decently well. And then you have to hope that the first shot lands very well, otherwise your opponent might not get too much damage at all for such an expensive unit. Against garrisons the issue remains the same. The third option to use it against static buildings like bunkers is also bad, because you could do more damage with the normal mortar. Additionally the low ROF makes it vulnerable to rocket artillery in the late game because it sits at the same spot for 40 seconds. The only virtue of the longer range, slow firing barrage is that you cannot be counter mortared and have a long area denial.
Yes, it has a bit more range, but only for the barrage and as I explained the barrage is quite shitty in most scenarios. The autofire on the unit might be fine, but the barrage is not. And this is exactly what balance team wanted to move away from and redesign mortars as support units that need active management. Ever since that patch, the 120mm became very bad, because it was hit by the damage nerf harder than all other mortars but cannot really support better than the standard SOV mortar. It's probably even worse due to the lack of flare at vet0.
And one last thing which I am not sure about though: I got the impression that it is more clunky to use. It needs to turn more often and/or at least has longer setup times.
Your arguments against the 120mm barrage are very much reasonable; however, I don't really agree with your conclusion.
Sure, the barrage ROF is lower than that of other mortars, but the actual difference is smaller than portrayed here. It does fire 20% slower than the PM-41, which translates to ~1.5 s more time for the target to move out of the firing line after the first shot lands. And while this may or may not make the difference between dodging or eating another shell, it could be
argued that most players would reposition early enough to not get hit by a second barrage shell from any indirect source anyway.
Therefore, the first shot is what counts most for any source of indirect fire against a non-static target, and this is where the 120mm barrage is superior to any other mortar in the game. Due to its relatively low scatter (only the PM-41 has ~6% less scatter area) and far better AoE profile it has a much greater chance to deal at least some damage to the target and will on average drain more HP with its first shell than any other comparable indirect fire piece except the Pack Howie.
Still, I agree the barrage is way less stellar against garrisoned troops and emplacements for the reasons you laid out above, and I'd also like to see some buff in that department - either by a different vet1 ability or slightly improved ROF with vet as suggested by others.
However, I think the main area the 120mm is lacking in is its horrendously long setup and tear down duration in conjunction with having to pack up and reposition for even the tiniest adjustment of firing direction. Since other mortars can even pivot in-place to adjust aim, maybe a justified buff for the HM-38 would be to reduce setup and tear down times a bit to compensate for the poor angular tracking capability?
All in all I don't feel that the 120mm is in a good position. You pay more to get a mix of slightly better performance in some circumstances but also much worse performance in other aspects. There is no real benefit and no real situatuon where it is consistently better than the normal mortar, especially conaiderung the quite hefty price.
Agree fully that the HM-38 is a bit lacking in total, especially considering the bang you get for the buck. Still, I'd say it does have its use in certain situations where it clearly outshines its smaller 81mm cousin, it's just not a flat-out better (or worse) option in every game.
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