The BAR was big, heavy, had a low sustained rate of fire...
(due to using 20 round magazines) but had good knockdown power and was reliable. While it's true that the BAR used a big round (30-06 if memory serves), the size and weight of the magazines limited the amount of ammo each BAR gunner carried. It was a good weapon in its day but isn't the kind of weapon that a modern infantry squad would want to carry. On average, you can probably carry at least 3 rounds of 5.56 for every 2 rounds of 7.62. Having more ammo is generally considered better than less. Carrying a long weapon like a BAR or M-60 is a pain, both in an urban environment where space is tight (and the need for long distance shooting is primarily limited to snipers) and in the bush where they get tangled (been there, done that).