Now that you mention it, I think having players design the size of the groups seems superfluous.
How about all sizes are unlocked at the beginning, but the size depends on the labor cost?
If you have the option of all sizes, and are not pressed for time, there is no reason to not always use the largest unit size possible. 9 person company is and always will be fully 3x as good at dealing damage than a 3 person unit, and will have 3x as many hps, so it will take 3x as much damage to kill them than a lowest size unit.
I personally prefer the balance and flavor that comes with predefined units, but that's not what FE "is". It is more an RPG game, and choices like unit size are good. They should, however, be choices instead of just "biggest unit always", or "research up to groups of five and call it good".
I really like the OP's suggestion that there be abilities which are limited to smaller groups which help balance them against larger units.
Alternately, if you split the encounter XP up by individual, and make the larger units take more XP to level, that could balance really quite nicely.
It would make a level 3 unit of 3 roughly the same as a level 1 unit of 9 in terms of soaking ability, and since they would lose their "models" at a lower rate than the 9 person unit, would retain combat viability across a larger portion of their health over time (more total hps per model offsetting more total damage output of the larger unit).