Each rifle barrel is an individual, and behaves slightly differently. However, there are some generalities that hold true.
Copper fouling smooths the barrel, to a point. Lead fouling is "lumpy".
A clean unfouled barrel usually shoots to a slightly different point of impact than a fouled barrel. Some rifles settle down after a single fouling shot, others take a few shots before they get consistant.
When fouling reaches a certain point, accuracy diminishes. So, for best accuracy, you need some, but not too much fouling. And what the right amount is, is different for every rifle.
I have known accuracy fanatics who clean bores completely after 20 rnds. Most of us only do it when accuracy starts to decrease. With .22s, it can take dozens, or sometimes even hundreds of rounds for a barrel to reach the point of max accuracy, but .22 rimfires are a bit different than centerfires in this regard.
I know hunters who will not clean the bores of their rifles at all during hunting season (unless they get dunked or something similar), simply because the cleaning will change that all important first round point of impact. They sight the gun in, and leave it (the bore) alone all season.
Another old timer trick is leaving the gun in the cold. Taking the gun into a warm cabin or tent at the end of the day means condensation (water) will form on the metal, and even inside the action. This is a bad thing, because it means the gun has to be taken down, wiped clean and oiled, or problems can result. And not just rust. Water in the mechanism will freeze when it goes back out in the cold, and causes trouble that way, as well.
What your .308 is doing is normal, if a bit on the upper end of the normal range. Now that you know, its easy to live with, just consider it a quirk of the gun.
We have a built in bias about cleaning our guns. This comes from the hundreds of years of shooting only black powder, where NOT cleaning the gun as soon as practical after use meant damage to the bore, and eventually the rest of the gun as well. And the military's phobia about a dirty weapon adds to it. Now, there are good, and sound reasons to clean everytime it is possible, but most situations ordinary folks have don't make it a necessity.
Enjoy your .308, and clean as you see fit. Maybe try differnt things and see what it does, and doesn't do. Once you know, its just a matter of doing (or not doing) what gives the best results for your use.
All else being equal (and it almost never is) bigger bullets tend to work better.