You're correct in that the 06 is a bigger cased cartridge. The 308 is an extremely efficient cartridge which is why the military adopted it. Because it is so efficient it holds its own against the bigger round until the bullet gets too long.

The 308 is also the base cartridge for the 7mm-08, the 358 Win, the 260 Rem and the 243 Win. Necked up or down it is and will always be a really good round. If I wanted a mid power 30 cal, I'd jump on a 308.

And it comes in a belt feed too. The M-60, the M-48, the M-240 and the MK-44 are all 7.62 Nato which is the military designation for the 308. The military knows what works.