The same differences could be done by varying other attributes.
No they can not. Firstly, because different damage has different effects. For example one of the reason Bolstered Infantry Sections are so effective is because they can potentially deal 80 alpha damage (5x16), which could alpha/burst kill a model in one volley. That is why all other 5-6 men rifle squads do not deal 16 damage per rifle. Alpha damage is also generally more important in (heavy) cover fights than accuracy, which is why a small long range squad like Grenadiers needs to have high (16) damage.
This dynamic was pretty straight forward in CoH 1, where Riflemen and Volksgrenadiers had the same accuracy and damage as each other at vet 0, but Riflemen fired slower at long range and faster at short range while Volksgrenadiers fires at about the same rate regardless of range. This was easily understood by the player and was also a more realistic way to balance the interaction between the two units.
And Grenadiers had higher damage with the same Kar 98K rifles as Volksgrenadiers, because they needed to feel like a significant upgrade, while having only 4 models, without having over-the-top visual stats (laser accuracy or insane ROF).
So secondly, accuracy and ROF are way less adjustable (without making units feel artifical) than an invisible increase in damage per shot. In CoH2 most infantry rifles already have 65-80% accuracy, increasing to 80-90% with veterancy (Obers Kar 98Ks even go above 100%), so there is no wiggle room there. That only leaves ROF, but that would need to be unrealistically high to facilitate a large increase in DPS. And as I mentioned above alpha damage itself is an important factor in balancing units anyway. There's also the difference in the amount of rifles/models in the squad to account for (from 4 up to 6). So in summary, again, varying damage per rifle is very important for gameplay and balance and it can't simply be standardized.
Also I'd personally say that the price of a unit is self explanatory for their performance, even if they share the same weapon with other cheaper squads, and the average player probably won't have a clue whether it's accuracy or damage that is different anyway, so there is no need to change it (and essentially make tuning balance and gameplay harder).