Not really, the current meta is to spam as much shermans as possible because even with BARs riflemen quickly become a nonfactor againts LMG grens, especially because CAS gives the ostheer player so much munis.
Againts OKW it's a different story, they generlaly lack good anti infantry options, but theres really no reason to pick BARs over m1919s or flamer rifles, considering that BARs are worse than both.
With the new patch where USF teching is delayed by quite a bit we might see a bit more BARs and maybe zooks, but i doubt it.
Generally, if you go airborne, rifle company or infantry company do not research BARs.
If you go armor company, do research BARs. If you have a massive amount of munis, going BARs to equip your rifles if you are airborne company might be a good deal. Pathfinders with BARs are quite good, too.
Other two doctrines are complete trash so i dont consider them
I would go BARs on Airborne solely for pathfinders.
They shred with BARs