By the true technical definition of assault rifle, they shoot intermediate rounds, not full power rounds, the actual caliber of the round has little to do with it. Assault rifles are short to mid range weapons. Most engagements are 300 yards or less. Even though assault rifles with the right ammo have an effective range for 500-600 yards, typically you are using you DMR and SPRs for longer ranges OR better yet, air strikes, artillery, and mortars.
.300 is just a number. There are many many cartridges that use .300 caliber bullets. Some of them are intermediate rounds, suitable for assault rifles, such as the 7.62x39mm or .300 BLK. Many are full power cartridges that are suitable for BATTLE rifles, DMRs and sniper rifles, such as the .30-06 Springfield, 7.62x51mm (.308 Winchester). And there are some high power, such as .300 win mag, that are suitable for long distance sniper rifles. Then there .30 caliber rounds, such as the .30-30 winchester rimmed cartridge that are used in lever action rifles that are not suitable for the modern battlefield at all.
5.56 is very suitable for the an assault rifles, for two reasons:
1. Low recoil, easier to control in burst of full auto mode
2. Lighter weight so the warfighter can carry more ammo.
It is so suitable in fact that during Vietnam after the Soviets saw how effective the .223/5.56 cartridges were, they redesigned their .30 cal 7.62x39mm AK-47s to use a 5.45x39mm cartridge in their AK-74, which has been the basis of their standard issue rifles even today.
I would not use the word "scuffle" to describe any type of firearm ever. You don't scuffle in lethal combat.