5.56 is quite OK for rifles/carbines, as is 5.45 and 5.8.
All are iffy for LMGs.
LMGs need be controllable on bipod out to about 300 m for suppression of window positions etc, so those low impulse cartridges make some sense for LMGs.
My question is why you think that the demands on the external or terminal ballistics of a LMG are or should be different than for rifles/carbines?
Pity Anthony Evans drifted away. This is right up his alley; he had good ideas about a medium-caliber cartridge.
Lots of people did so, particularly intermediate cartridges above 5.56 were fashionable ideas for a long time (especially 2004-2010 or so).
I myself argued in favour of a medium cartridge between 5.56 and 7.62 for dismounted forces and an intermediate cartridge between 7.62long and 12.7 for mounted forces / vehicles.
The ~7mm cartridge would address the terminal ballistics concerns about 5.56 and the ~.338 cartridge would defeat all those plating that was meant by design to resist 7.62, but not 12.7 (~STANAG 4569 level 3) and be generally more useful through brick walls.
Nowadays I'm more focused on getting the weight for infantry and scouts down, so I'm fine with the current puny cartridges for carbines and LMGs.
(The first time I saw a 5.56 mm cartridge sometime in the mid-90's after being trained on G3 / MG 3 I thought it was a cartridge for the FN P90 - it looked so tiny!)