I never really figured why the military got rid of .308.
The US military got rid of 308/7.62 NATO rifles for the same reason the combloc got rid of 7.62x54R, because they wanted an assault rifle. Fullpower rifle rounds don't lend themselves to full/burst fire in anything lighter than a BAR or RPK. 5.56/5.45 rounds were chosen (eventually chosen in the case of the 5.45) for lightweight, low recoil, and flat trajectories.
BTW, shooting through heavy cover isn't the job of a battle rifle whether bolt or semi. It is the job of a light, medium or heavy machine gun. Semi auto rife through a block wall or thick wood is not effective. Think your going to punch through medium cover (actually concealment as someone else said)? Not gonna happen. You probably don't even know what part of the wall or whatever the person is behind.
As for civilians, a 308 makes more sense because you aren't carrying a full battle load and aren't likely to have a full auto weapon. The biggest advantage of a 5.56 (or 5.45) weapon for a civilian is the lightweight of the system. For me, another important consideration is familiarity. I've shot almost everything and carried several different rifles, but an AR just feels right in my hands. Lightweight and accuracy are always an advantage. And I have a supply of 5.56 ammo, so my choice is easy.
I simply don't feel there is any chance I'll ever need a rifle for the long range shots some guys hypothesize needing. If I did somehow think I needed a long range rifle, it wouldn't be a semi. That doesn't mean that I think 308 is a bad choice. It's obviously an excellent round available in some excellent battle proven platforms.