The major reasons for the AK's lower grade accuracy is that it was never intended or engineered to be an accuracy rifle.
The reason for the lower accuracy is the much looser fit of parts, which increase reliability at the expense of accuracy.
Without a complete change of the AK's basic design, you're not going to get great accuracy out of one.
Other factors for lower AK accuracy are the terrible sights and trigger.
One major factor in AK accuracy IS the ammunition.
The ammo is not loaded for accuracy, it's loaded to be cheap and reliable.
Soviet era ammo was specifically designed to work in their weapons, and their weapons were designed to work with their ammo.
Their ammo is steel cased.
In order to allow better reliability of feed and extraction, the cases have more of a taper than western ammo.
The more tapered case does make feed and especially extraction of steel cases more reliable, but the ammo is inherently less accurate then the straighter cases of western ammo, which is made of brass.
This is one reason many western firearms have trouble with extraction problems and broken extractors when used with Soviet design steel cased ammo.
Western firearms and ammunition designs gave no thought to the use of steel cased ammo, and when steel cased ammo is made in western design straighter wall cases, they often have extraction trouble.
So, changing the caliber of an AK to a western ammunition design like the .223-5.56 you will often see at least a tiny increase in accuracy.
However, the basic design of the AK was oriented toward reliability, not accuracy, so until the rifle is redesigned you won't see an AK target rifle.