The primary hunting rifle throughout the history of firearms has tended to be an inexpensive, accurate, mass produced rifle of the previous large war with a simple reliable action which had become surplus.
Large wars typically resulted in new technology and after large wars there was typically a large number of obsolete but well made (designed and improved to be rugged on the field of battle) rifles that would go to civilians.
These often then became popular well made and inexpensive hunting platforms.
This of course has changed in modern times somewhat because now the military will crush retired firearms long before giving them to civilians as surplus (even civilian legal semi-auto firearms.)
With restrictions on select fire, and as modern military rifles typically have select-fire the standard rifles of the world cannot simply go to the surplus market.
WW2 rifles in general are the last that followed the age old tradition of going to civilians.
Yet we still see the civilian market trying to trend the way of the past with the AR gaining popularity as a hunting platform, and people taking them to the field where the can.
Select fire AK-47s even see use in hunting in the former third world, or poaching as is often the case as the guns themselves are often illegal. For the same reason: they were mass produced, are reliable and when retired hit the market in such large numbers at inexpensive prices that a lot of people had one.
What will be most popular is now less predictable because laws and restrictions keep surplus from going to civilians, but for most of the history of the firearm the most popular hunting rifles were the military arm of the previous decade.
In the American colonies, in the early USA, and in much of the world.
World War 2 was the end of this trend, and it ended with a lot of bolt actions.
At the start of World War 2 most nations were equipped with bolt action rifles. During World War 2 these became obsolete.
After World War 2 they flooded the civilian market and dominated the cheap reliable hunting niche. While no longer as inexpensive as surplus, they have remained in that position.
If all the battle rifles had flooded the civilian market when NATO switched to the 5.56x45 as the standard caliber, then accurized FAL and M14 actions in 7.62x51/.308 would likely dominate hunting today.
Instead president Clinton had most of them crushed.
Due to legislation civilians are no longer trustworthy enough to have the previous generation's standard military arm. A break in tradition from the previous centuries.