I see a lot of people in this thread lack any sort of nuance. Unsurprising.
Let's start by saying the balance team was dealt a bad hand. A lot of the issues in Coh2 are the result of bad faction design. Brits lacking essential tools to deal with basic things, and instead having to rely on dumb and op designs that are neither fun to play as nor against. OKW too shares some of these issues. You can get superb light vehicles, or you can get healing. That is simply bad design. The game should not lock you out of essential pieces of the game. USF is the closest expansion faction that has a somewhat reasonable design, but that required a lot of reworks by the balance team. In an ideal world, the factions would be have been designed like they seem to be in Coh3. Yes, you can go to T2A or T2B with the Wehrmacht in Coh3, but neither will lock you out essential things like light vehicles or AT guns.
Another factor that made Coh2 incredibly hard to balance are the poor maps (this is mostly an issue in 2v2 since it has the poorest and most neglected map pool, but I guess it can be in 3v3 in 4v4 too). When all maps are laney or wide open fields with no flanking, that typically favors Axis. Half of the 2v2 Maps consist of this, which means USF has a very hard time against something like LMG Grens. How do you balance such an issue, since it has actually nothing to do with balance per se?
Finally, it probably didn't help the balance team had to balance around all four game modes. But not only do they play differently, but there is a vast difference in skill between the average 1v1/2v2 player and someone who mains 4v4. Here, the balance team made the right choice in trying to focus on balancing 1v1 and 2v2, since you cannot balance the game around people who have a fundamental lack of understanding of the game.
With that said, while the balance team was dealt a bad hand, they didn't play their cards particularly well either. A common sense solution to make Brits more viable would have been to make the Land Mattress stock. But we know from the balance team that Relic vetoed that idea. Yet their in response was to add the miserable heavy mortar pit barrage, which just doubles down on the terrible design.
There were a number of very strange decisions, that they should have known were bad ideas. Buffing the Sturmtiger and making it to as close as an I-Win-Button as you can get was completely inexcusable. Units like the Sturmtiger, AVRE or B4 should not be competitive units that allow you to one-click an opponents squad.
Buffing the 120mm Mortar, while at the same time nerfing Counter-Battery should have been obvious omen of what was to come. It's a testament to how broken the 120mm is that the ML Mod had to nerf it because it breaks the game on a competitive level. And now 1v1 and 2v2 automatch is forever sttck with this brokenly OP, 2 CP mortar that, as it so happens, is in the best Soviet doctrine.
When it comes to reworking infantry, outside of two examples, the balance team had to, in some way, revert every single one of them, because they turned out to be too god. Examples: JLIs, VSL Grens, Fussis, 7 man Cons, Tommies (multiple times), and so forth.
Speaking of Cons, I want to talk about that change in particular, because I think it's the root of virtually all power creeps in the game. The 7 man conscript change just absolutely atomized the infantry balance in 1v1 and 2v2, to the point Cons received multiple nerfs in virtually every patch, but still are probably the best mainline infantry in the game. The other thing it did was to give the Soviets several indirect buffs. Because Cons were now viable, Penals were no longer needed. Therefore, every Soviet now had access to T2, rather than T1. Unlike Penals, 7 man cons don't bleed, because they build green cover everywhere. Green cover they can place for Guards, and then merge into, further reducing bleed. Combine that with the hyper-effective T34/76, and you now have a faction with by far the most options, strategic depth, and comeback potential. It also made it so that 3 out of 5 factions will now just plaster the map with green cover everywhere.
But the worst part is that that change meant that both the Axis factions, in particular the Wehrmacht, received buffs that they shouldn't have in order to remain competitive. This in turn left USF and UKF behind in the powercreep, to the point where they have mostly disappeared from competitive play in 1v1 and 2v2 (outside of a certain USF doctrine, which I'll get to in a second). OKW's aforementioned awful design has also played a part in why it disappeared from competitive play in 1v1.
But of course I have to get to the one thing that ruins 2v2s and up far more than anything else. Namely, the combination of the Scott buff with USF Airborne. Anyone with half a brain can play Pathfinders and get a decent rank with them. And that's not necessarily on the balance team. After all, they changed Pathfinders years ago, and it took forever for people to realize that they were good. But what is the balance team's fault is that they, for some utterly bizarre reason, decided to throw in a Scott buff (a unit that was buffed three patches in a row, no less) into what they knew was going to be the very last patch. And this is what made the airborne build so powerful. Before, you could counter it with Obers or team weapon spam as Wehrmacht. Now? Your infantry gets deleted by the Pathfinders, your tanks rendered useless by the Jacksons, and your support weapons more or less two-shotted by the Scotts. In other words, they introduced an experimental change into a patch that they knew they would not be able to fix.
Again, not all the balance team did was bad, and anyone who says that the game would be better off without them is, quite frankly, an idiot. All the QoL changes were excellent additions, and by and large, the balance team has done an excellent job with commander reworks. But ultimately, the current meta that is the result of the balance team's work, is probably among the worst it has ever been.
Tl;dr: The circumstances in which they had to balance the game was poor, but they didn't do a good job either.