I suppose more has been written about cleaning bores than about any other rifle topic.
If you care, the acquisition of a borescope will change the way you think about this. Some rifles foul more quickly than others. Much depends on what bullets you're using. Not everyone is trying to treat the same problem.
Thin copper-jacketed match bullets in a match barrel can go hundreds of rounds without having much effect. Solid monolithic copper bullets in a rough barrel can foul impressively after only a few shots. Does it matter? Depends.
As has been said, stripping all of the copper away may not be such a great idea..... and with many barrels it's darn hard to actually do unless you use an ammonia-based solvent and a bunch of elbow grease. I've tried Boretech Eliminator (and their copper variety) and I think it works OK-ish. I've been shooting TSX bullets in my CZ550 .416 Rigby and the copper buildup was visually impressive in the borescope after 50-100 rounds. When I first peeked, it looked terrible and I set about trying to correct a problem that probably didn't need fixing. A couple of hours of scrubbing with alternating patches, plenty of Eliminator, and nylon brushes helped a little, but I eventually decided it wasn't worth the trouble. The rifle was grouping well all along.... so why bother? These days, I just give it a little TLC with some Hoppes.
The Bartlein barrel on my .300 WM accumulates only a slight copper wash after 50 or so Berger HVLDs. It cleans out sooooo very easily with just a few patches. As has been said, I don't obsess about it, and I worry far more about carbon. That's pretty easy to remove, but it's basically impossible to know what you're actually doing without sticking a scope in to look, especially in the throat region. With a nice match barrel, one or two fouling shots after cleaning seems to suffice. My .260 AI started acting funny a while back and it had developed a pretty good carbon ring. It took a bit of effort to remove, but it seemed to fix the problem. Without a scope, I'd would have had no idea what happened.
Shooting 100 .223 rounds through my AR-15 with a suppressor produces a tremendous mess. Gas blows crud back into the action, down the magazines, and everywhere. For that, there's no easy solution except for a good de-greaser or heavy solvent like brake cleaner. I always apply a generous coat of oil after that (Stoners like to run wet). I'd hesitate to get any degreaser near a nice wooden stock.
For the average guy, I'd run a mild solvent (Hoppes #9, etc) down the barrel after every box or two of ammo. This will remove carbon, and is very unlikely to cause any harm. Less is more. Be sure to completely dry the bore before firing. I prefer a single-piece carbon-fiber cleaning rod and simple jags with cotton patches. Be especially careful in the last three or four inches before the crown. Work patches one way, preferably with a quality bore guide. If groups open up, I'd take a look with a scope before jumping to conclusions. If you live in a humid area, consider leaving a light coating of oil in the bore but patch it out before you shoot! Always leave a light coat of oil around the action and other exposed metal, but not around the trigger assembly.
Just my $0.02 from 40 years of shooting - mostly long-range stuff these days. The average US hunter might need to clean the bore every few years.