Interesting suggestion here that the NATO-standard 5.56x45mm infantry cartridge was selected based on short-range engagements that prevailed prior to the proliferation of rugged magnified optics. I.e., since it was hard to see and hit an enemy more than a couple hundred yards away, the 5.56mm cartridge was considered adequate.
Ever since its adoption field reports have complained about its marginal stopping power. In recent years our military has spent a lot more time in wide battlefields with optics good enough to reach out to and beyond the nominal 400-yard “effective range” of the 5.56mm. It may weigh twice as much, but nobody questions the ability of 7.62 NATO to stop human targets out to 800 yards. (Beyond that is the realm of trained snipers, who may step up to .300 Win Mag or .338 Lapua Mag cartridges with effective ranges beyond a mile.) There has also been a lot of recent work on other cartridges that fit within the 5.56x45mm profile but provide better ballistics and stopping power, 6.8SPC being the most widely adopted of that family.
Update: As further evidence of 5.56 inadequacy at longer distances: One range I frequent hung steel plates at 600 yards using fire hose. One day I noticed several .223 bullets stuck in the hose nose first: After 600 yards of flight they retained so little speed they stopped in the first layer of rubber!