Why bother, well weight was the main reason, how many rounds can soldier carry, plus 30-06 with its long action wasn't working well in new submachine guns, rate of fire was limited. But when they tried rapid fire with 308 the recoil was enormous, so it was quickly changed to 5.56 nato.
Wikipedia:
Work that would eventually develop the 7.62×51mm NATO started just after World War I when the large, powerful .30-06 cartridge proved difficult to adapt to semi-automatic rifles. A less-powerful cartridge would allow a lighter firing mechanism.
The T44 was adopted as the M14 in 1957. Britain and Canada adopted the FN FAL around the same time followed by West German army as the G1. The Germans soon transitioned to a modified version of the Spanish CETME rifle, Heckler & Koch G3. With all three of these firearms, it was clear that the 7.62mm NATO could not be fired controllably in fully automatic due to recoil. Both the M14s and FAL would later go through several variations intended to either limit fully automatic selection through semi-auto version or selector locks or improve control with bipods and/or heavier barrels.
When the M14 arrived in Vietnam, it was found to have a few disadvantages. The rifle's overall length was not well suited for jungle warfare. Also, the weight of 7.62×51mm cartridges limited the total amount of ammunition that could be carried when compared with the common 7.62×39mm cartridge of the Type 56 assault rifles, which the Vietcong and North Vietnamese Army soldiers were equipped with. In addition, the originally issued wooden stocked versions of the M14 were susceptible to warping from moisture in tropical environments, producing "wandering zeroes" and other accuracy problems (this was fixed with the adoption of fiberglass stocks).
Fighting between the big-round and small-round groups reached a peak in the early 1960s, when test after test showed the .223 Remington cartridge fired from the AR-15 allowed an 8-soldier unit to outgun an 11-soldier unit armed with M14s. U.S. troops were able to carry more than twice as much 5.56×45mm ammunition as 7.62x51mm for the same weight, which would allow them a better advantage against a typical NVA unit armed with AK-47s.