In my opinion, the adequacy or inadequacy of the 5.56's lethality could be argued all day, but in the absence of any satisfactory scientific studies on the matter, the only things that can be provided are anecdotes.

That said, there are more concrete and indisputable attributes of both 5.56 and 7.62.
To isolate 2: The 7.62 provides superior penetration of light cover, potentially allowing troops to end the engagement faster. The 5.56 allows a greater amount of ammunition to be carried, letting them operate longer without resupply.

All very obvious stuff. My question is... If we were to go back in time to 2003 and make 7.62 the service cartridge, would we have been hearing about troops running out of ammo in 2 minutes instead of insurgents taking 30 rounds and not falling? (Hyperbole was intentional)

I often hear something along the lines of, "You cannot carry enough 7.62 in a modern war!" I've never heard an actual quantitative figure stated. How much ammo do you "need" exactly? I realize there is no "average" firefight, which makes the answer to that question more elusive. However, the less that number is, the less the difference in weight between those 2 cartridges. Something to keep in mind.