More similar working armies

I think the general sentiment here is that factions should have access to things that do the same thing (light indirect fire, mines, MGs, AT guns, etc.). For the most part, they all do. Brits need some sort of rocket artillery because it's so much better than traditional artillery in coh2. USF has some issues with the non-linear teching and non-doc mines, but the USF stuff is good, like Lemon says.

Asymmetrical balance is good; it makes each faction seem interesting, fun, and new, while (theoretically) not harming gameplay or balance. Ease of access to necessary or extremely helpful tools (snipers, ATguns, etc.) is crucial and often an issue.

every faction has serviceable HMGs and AT guns (dont say the 50cal is shit, its not. dont say the USF at gun is shit, its cheaper than a pak and also has great veterancy). you can argue that the leig/pack howitzer are different than mortars, but theyre still most definitely indirect fire. the brits definitely get the short end of the stick with the mortar pit, but its still 2 mortars no matter how you look at it.

the only thing that some factions DONT have are snipers (even then there are pseudo snipers like pathfinders anad JLI) and UKF dont have rocket artillery or flamers.

the .50cal is a good weapon but the crew has cost/durability issues. the 57mm is fine against mediums but has scaling issues against anything bigger than a IV, which is a problem because the only effective AT weapon against Vs/heavies that USF has costs quite a bit of fuel (there isn't a balance issue with the jackson, it just makes it harder to get out than an AT gun) and can only fight vehicles by kiting. OKW doesn't have a non-doctrinal MG and even when it suppressed the kubel was a less effective suppression platform than a setup team after the first couple minutes. brits have the mortar as mentioned. the lieg i consider generally better than a mortar and i haven't used or seen the pack howitzer in long enough that i'll avoid commenting on it.

the problem with not having core units up to standard is that the game design assumes that everyone has these standard units and so situation that require them are disproportionately difficult for factions missing core units.

snipers i don't care about; they're not a core unit.

tl;dr: factions can work without the core HMG/mortar/AT gun trio but it makes the faction gimmicky and gimmicks are not good for gameplay. i'd rather have similar, but solid, factions then ones that are frustrating in certain situations; asymmetry is good but only to a certain point.

Each faction should have an area of combat they excel in, but all should be balanced at all game stages assuming equal map control. This will be long but I'll try and explain imo the way each army should be for a balanced and *fun* game.

Ost: long range combined arms type play, versatile and powerful units that depend on abilities and upgrades. Late game Ost combined arms dies to all arty, but to compensate currently they get God armor. Buff viability of Ost support weapons and non ostruppen infantry lategame so panthers, stugs, werfers can be nerfed.

Sov: close to mid range Zerg units mixed with select good ranged units. Should gain economic edge by building the most mp efficient army, with units that are ok at one thing but are wiped/killed a lot. Instead, soviets gain economic edge with their high end wipe tools that aren't fun to play against and nullify lots of mid/late Ost combined arms.

Usf: average prices, close to mid range combined arms types units that are versatile, powerful but less survivable than all counterparts. Should gain economic edge through use of smoke and vehicles to harass enemy economy, until usf army is better than enemy army and usf makes a huge combined arms smoke push. Think of protoss economy in sc2. I'd say usf are the most fun and balanced ingame army in this regard.

OKW: fast, expensive, specialized units that are good from far away or at in your face range. Should gain economic edge by literally killing enemy units, to offset the fact that OKW units are insanely expensive. Instead, OKW economic edge is cheapest teching and select super cost efficient units to offset the fact that many OKW hits are overpriced/lack luster.

UKF: slow, super tanky long range units that are ungodly expensive mixed with rare skirmishing units. As of right now ukf gains the edge economically by surviving to their lategame lol, they lack "economy." UKF economy should be focused on scarce territory and not expanding, but gathering for attacks with most high end units ingame. Once sufficient army created, damage to enemy huge.

Playability/ winnability seems very stronly dependent on things like size of map and number of players.

I mean you're going to get your butt raped on large maps like Red Ball Express if you're all Soviets against OKW, on the other hand things will be different if it's UKF/ USF against Ostheer.

This does't really have anything to do with faction roster and their play style, but it does show that a factor in winnability involves not just unit design but map size design, and it seems Relic didn't take them into account when they make or balance faction design. Hell some maps like Rostov are simply unbalanced purely by which side of the map you start.
If they balance a faction from a large-map perspective it will ruin small-map design, and vice versa.

In any case I disagree with OP, the ideas and usability of the vanilla non-doctrinal support weapons exist in the newer factions. Plus I find it refreshing to play a faction like OKW where you're not entirely dependent on a build order that requires an HMG, a Mortar, or AT gun. Yes you WILL need suppression, indirect fire, and AT capabilities, but OKW/ USF/ UKF already provide those. It's not like you can just volksblob your way to victory points ignoring HMGs and indirect/ AT fire, so it's actually a drawback if you ignore those mechanics or fail to provide tactics that deal with or utilize them.
Myself I've played without HMGs or Mortars or AT guns as OKW, and it's as often not pretty than fun, because while it's not the usual build MG42/ PaK that I spend a year playing Soviets/ Ostheer, it also can make things harder because you don't have them and need to scrounge them up from the enemy. That's fun. If I REALLY needed HMG, I can choose one of two commanders.