I have played almost every single RTS game starting with the original Command and Conquer. One of the things that Company of Heroes 1/2 does well compared to other RTS games is that you become emotionally invested in your Units due to the Veterancy system. In Starcraft if I lost a Protoss Zealot, Zergling or whatever unit it didn't really matter as it was just resources that I could easily replace.
I bring this up because the officers being "free" as part of your tech basically make these units the same as that Starcraft Zealot or Zergling. I don't really care if they die since they were free and they gain Vet much faster than Riflemen so losing them doesn't have that same emotional impact as it does when losing a Vet Rifle Squad does.
This is one of the things about USF that I dislike the most and would like to see changed. I agree with you that LT/Captain should be made into support units. They should be vital to USF and not just a Rifleman clone without a soul that you do not care about.
Losing "free" Officer Squads and having to pay for them would be a fair trade if it meant USF had easier access to HMG/AT Gun and making the LT/Captain have some useful abilities built in since you would be paying for them instead of getting them free.
Assuming No New Abilities (Even though it would be easy to make new abilities)
Infantry Company
The M191A6 LMG Replaced with Advanced Infantry Equipment
(which gives Riflemen Flares and Rear Echelon Flamethrowers) Thematically it would work
Tactical Support Company
The M191A6 LMG Replaced with Rifleman Field Defenses
Same as above from a Thematic point it would make sense if you could drop mines/make sandbags as part of the "Support" or "Tactical" theme going on with the commander.
Both of these would fit these commanders well without changing too much.
Incredibly based. RET flamethrowers are a blessing upon the faction.
EDIT: I would also like to add that LMGs unlocking with major is a great idea not only because it gives USF some nice late game power, but also because also it's a risk/reward, being that in order to outfit vetted riflemen with LMGs, you'll have to hold off on giving them double BARs.
However, one unforeseen consequence of this might be RETs synergy with M1919s and Volley Fire. Oft unused, in my opinion it's only overlooked because it's restricted to two less than meta commanders. With good micro and positioning RETs can 1v1 any unit. Being introduced into stock might make it a combo that should be "looked", to borrow another's words.