The rope creates friction. The fibers in said rope are abrasive. When the rope gets dirty it is even more abrasive. It is next to impossible to get the abrasive grit out of the rope once it gets dirty. The carbon residue from inside the barrel is harder than the steel as well.
I can remember a Portuguese Colonial Sergeant jamming his boot half way up a recruit's butt when he insisted the pull through material was to soft to harm the crown of his rifle and couldn't be bothered to use a muzzle cap/protector supplied with the rifle. More rifles have had their accuracy destroyed by POOR cleaning techniques than any other cause.
Why do you think so many old Mosins/Mausers/SKSs/Martinis/Springfields etc are counterbored???? The counterbore was done to make an other wise accurate bore serviceable again after some troopie for some unknown reason used POOR cleaning techniques. I have seen more than one fellow use pull through cords and pull them to one side of the muzzle, rather than straight through. It is a recipe for disaster down the road.
This is something to take note of. The so-called "boresnake" is just a modern version of the old pull through cord with all of the same perils associated with the pull throughs. Cdn Army EMEIs on the No4 rifle dealt with barrels with ruined crowns/degraded accuracy as a result of cord wear. If the bolt can be removed to give access to the bore from the breech end by all means use a cleaning rod with a proper fitting patch rather than a pull through. If you can locate a bore guide to insert in the chamber and help keep the cleaning rod centered, so much the better.
I can still remember guys in the barracks cleaning their FNs with a pull through and getting the patch stuck in the barrel. Then they would tie the end of the pull through to a bed frame and give a mighty heave lodging the patch even tighter and maybe breaking the cord in the process. Good way to set themselves up for a blast of sh$t and have the rifle sent off to the armourer. There was a cleaning kit, which included a rod, issued to each section and that was the best way to get it done. We were still being issued the old 4x2 patches for the .303 which were a bit oversize for the FN. If you forgot to tear off a small strip before trying the pull through in the FN you ran a pretty good risk of getting the patch stuck.
A "frosty" bore, which is a polite way of saying a pitted bore, can still shoot well if the rifling is sharp and the crown is good. A pitted bore will, however, strip off more bullet jacket material and foul more quickly than an unpitted bore.