Interesting take on things. I have to admit that 3v3 isn't really an area I'm qualified to comment on, but I agree the Pershing - or mostly any heavy tank - isn't really enough of a shock unit to justify skipping things like a Calliope in larger team games. This probably has more to do with the size/layout of 3v3 and 4v4 maps, which have much higher unit density and don't play out like 3 separate 1v1s in most cases. Hence artillery is much more likely to find juicy targets, while heavies are much more certain to hit a TD brick wall sooner than later - but I don't need to tell you that of course.
I'd usually also have more than one tank in a 1v1, plus finding the space to spread your army out in wide flanks with CA active for both groups forming the pincer isn't too hard, either. So I guess this might be just another example where a doctrine/unit/ability is stronger in smaller game modes than in larger ones or vice versa. Far from the ideal situation for sure but I doubt any of the changes suggested so far would really make a difference in this case (unless we're talking all-out faction revamps of course).
I'm not sure if bringing the armor back to 300 together with the DR already implemented would be too much, but since we're still in the beta phase this might be a good time to test it and see if it sticks. I do however like the idea to buff the MGs a bit to match the DPS the Tiger and especially the IS-2 get with their respective pintle mounts. Right now the Pershing is pretty bad by 50% or more at any range in that regard.
If in beta, the 300 armour pershing + MG buffs prove too much alongside the speed/repair speed buff, then I'll hang myself by the ba**s from the nearest tree.
In 3v3s, you do sort of play 1v1 on "lanes" (so not as wide as 1v1) with a danger of being surrounded by another player. Great example is Rheine 3v3 bot VP/fuel. You secure it, have a couple of rifles there, captain and whatnot and another player can push through mid and completely surround your forces and pretty much wipe them on the long retreat path. We need new 3v3 maps or reworks of some 4v4 maps to fit the 3v3 format since most current ones are really really bad and promote rocket arty/LeFH spam with super heavies + KT pushing for the win (Hamburger Port, Ettelturd station and the likes. https://www.coh2.org/topic/108413/3v3-maps/post/865866). And yes, in 1v1 where the maps are wide and you're really only fighting 100 pop cap, you know what the enemy has or doesn't have. You know if you see a couple of PGrens and paks and a P4, that a Tiger is far off because there just isn't any population left. Also, using CA there, is quite easy and rewarding. So yeah, in one way, armadillo and Sander are right that CA should factor in, but also wrong because it's not an absolute. It costs muni and requires certain parameters to be met, which can be countered, quite easily in larger game modes (the blobbing around tanks part to get your money's worth)