Personally I shoot through a clean barrel instead of a fouled barrel because when I work up accuracy loads, They are fired in a cleaned barrel for each group
If you work up a load in a fouled barrel you must let the barrel foul before it will shoot your load accurately.
Fouling is by nature inconsistent because it is not uniform in it's placement. A clean barrel buy its nature is very consistent because the bore is clean and free of uneven deposits.
If you don't clean, after some point the bore will foul and settle in with some degree of accuracy and this is the way you will have to shoot to keep the accuracy you achieved with your load because that was the condition it was in when "The " load was found.
In some matches we were forced to fire 100+ rounds without cleaning and this was the reason we worked up loads for a fouled barrel. This match rifle was capable of 1/2 MOA groups with iron sites, But when the barrel was striped of all fouling, it would consistently shoot 1/4 Moa until it had enough fouling shots pushed through it.
Dry patching will work some of the time on some barrels that are pristine (No fouling) but others need one fouling shot and a dry patch to remove any oils or residuals before shooting consistent groups.
Ether way (Clean or fouled)is good if it gives you the accuracy you want But I prefer a clean barrel for best and most consistent accuracy.
Different strokes for different folks.
J E CUSTOM