The impetus for the 6.8mm round seems to be an Army requirement that a tungsten-free version of the selected caliber/cartridge be able to penetrate all known body armors at 500 meters, not just at point blank range. The best in class body armors in question appear to be recent Chinese and Russian developments.
The M995 tungsten cored 5.56mm cartridge is said to penetrate all known body armors inside 200 meters, but not beyond. It has also not performed consistantly at point blank range due to bullet stability issues. The M855 5.56mm cartridge and its developments are unable to penetrate best in class body armors at all ranges.
Penetration of body armors is believed to require a certain level of retained kinetic energy, which is why 6.8mm calibers have been selected. They are capable of delivering the retained energy desired at 500 meters.