I actually like the idea for a military application, if you could get the speed with higher BC projectiles, but the case length inside the AR15 doesn't allow it.
I'm pretty fond of .257", but haven't seen one that offers anything over 6.5mm that would justify them enough for me to invest in dies and projectiles for it.
The barrel is a very limited fixed cost and negligible to me personally.
Since there aren't any projectiles with good numbers on them compared to 6.5mm, it would only add another cartridge that can fit in my 5.56 mags, which I would have to implement some type of procedure to segregate in order to avoid any issues with loading one in the other.
For a replacement for 5.56, I like the idea, as there isn't really a noticeable recoil difference and you can get a lot of speed from the same case due to neck-to-case diameter ratio without pushing pressures.
It doesn't warrant enough change for military adoption, but probably would have been a better route to go in 1957.