Target rifle cleaning is as individual as the shooter. I know one F Class shooter, she is a National Champ in multiple categories, she claims her fouled barrels shoot tighter than cleaned ones and that she sees a clean barrel settling in. Her husband, who is her gunsmith, ammo loader, believes otherwise and it is a source of tension if he cleans the barrel.
I know Smallbore Prone shooters who clean "when the barrel tells them". I also see very good Smallbore prone shooters who clean at the end of the match, every day, before they pack everything up. In four day matches, (called 6400) I will clean the barrel out after the second day. Can't tell one way or another if it makes a difference. I drop shots due to poor position, bad wind calls, and jerking the trigger.
Everyone who cleans a rifle barrel uses a bore guide. I am aware of one Smallbore Prone National Champion who damaged his barrel, as a junior, by not using a bore guide. You want to keep the cleaning rod from rubbing the interior of the barrel. I don't recall seeing someone not using a brush, but it does not have to be a bronze brush, could be some nylon ones. I used bronze brushes and a bore guide on my centerfire rifles, sometimes I use a bronze brush or a nylon brush on a rimfire. Just how I feel. I can feel less resistance after a couple of strokes when brushing with a bronze brush. I don't know if I am actually pushing anything out or if the brush is getting smaller.
I have been told that if the accuracy in your centerfire barrel goes south, to clean with JB Bore Paste. Frank of Compass Lake says he sees compacted gunk in the throat, stuff that won't dissolve, stuff that has to be mechanically removed. He also said he had examples of fouled barrels that shot poorly until Bore Paste removed the gunk. I recommend using JB Bore paste sparingly as it is an abrasive.
Something that ought to be addressed is lubrication. Whether of not you clean the barrel of your rifle, you need to oil or grease the firing pin cocking cam. I have seen one, maybe two, Anschutz rifles that bound up because the cocking cam was not well lubricated. I am aware of one guy who dry fires the heck out of his rifles, they were Remington M700's, and he has worn out the nose of firing pin cocking piece noses, and I assume, also worn out the cocking cam in the bolt. I recommend grease for this area, I have been using Moly grease, there might be better, but you need to get the friction down.
In so far as cleaning the trigger mechanism, read the manufacturer's literature. A bud of mine, his $350.00 two stage trigger locked up. It would not reset. It was not a Jewel, I forget the brand. He had been cleaning it as through it was a Jewel. Jewel recommends lighter fluid. Bud's trigger, if you pour lighter fluid into the mechanism, it stays and prevents trigger reset. Bud found this out from the manufacturer. Bud took the trigger apart (I don't know how far) and got all lighter fluid and oil out, and his trigger works fine.
Based on discussions with Bullseye Shooters, I am keeping the sear surfaces of my 1911's and M41's well oiled. I am using LSA, a semi fluid grease, which has remarkable adherence to surfaces. These sear surfaces wear in these pistols and I want to get the most use out of mine, before I have to replace them. AMU shooters told me they wear out sears about once to twice a year, but they are firing around 7500 rounds a month.
I have seen Bullseye National Champions pushing a cleaning rod down the barrel every ten shots. They believe that if they don't, accuracy will deteriorate. Generally speaking, Bullseye shooters keep their pistols clean and well lubricated. It is not enough to just clean the barrel. Bullseye shooters shoot the lightest loads that reliably function the pistol, and, are accurate at the desired range. (I have loads that are accurate at 25 yards but not 50 yards). Regardless, dirty pistols won't cycle reliably. Bullseye shooters usually add a drop of oil on the barrel end every ten shots. And you will often see them adding more oil to the rails and cycling the slide at some point in the match. I was told an old adage about lubrication: " the elbow is the drip point"
Firearms are machines, they function better when clean and lubricated, cleaning is not all about the barrel, don't forget the rest of the mechanism.