Many years ago I was told I was an idiot because I thought the .250 Savage would make a great compromise round between the 5.56 and 7.62.
Somebody went through a lot of work to develop the 6.5mm Grendel in order to essentially replicate the ballistics of the .250 Savage :-)
Yes, I believe a .250 savage would have worked quite well, but the military, like all bureaucracies, has to do things their own way, usually creating more expense than necessary to achieve the same or, in some cases, poorer results than existing equipment.