99.9% of the time you are just carrying your rifle
The reason for the movement toward lighter rifles is that shooters realize that all most all of the time with a rifle is carrying it. I agree with you that firing standard cartridges 270, 308, 30-06 in something less than 7 pounds is not alot of fun. My Win 70 Featherweight in 30-06 with a laminated factory stock weighed ~7 pounds then I added a Leopold 1.5x5 VXIII and a nylon 1 1/4 sling. I think the current weight must be around 7 3/4 pounds. This rifle doesn't kick hard in my opinion. My brother in laws Ruger Ultra Light M77 in 30-06 started at 6 pounds, adding a Leopold 2.5x8 VXIII and a leather sling still has it ~7 pounds. The 3/4 pounds does make a large difference when you shoot the two rifles. I think that the Ruger American is listed at 6.5 pounds adding a scope and sling should make it into the weights where recoil will not be punishing. I would recommend reloads on the light side and bullets using 150gr instead of 165 or 180.