Much of what people refer to as "Carbon" is oxidized detritus from the bullet jacket and some from the actual case. Smokeless propellants leave very little residue because the Nitro-Cellulose (and Nitro-Glycerine) are compounds, not "mixtures" like black powder and thus, pretty much the entire propellant goes from solid to gas rather rapidly. About the only "Carbon" that may be in the propellant, apart from that in the "Cellulose" part of the "Nitro-Cellulose", is a tiny amount of Graphite used as a static electricity "suppressant" and "flow improver" in the loading process. Any stray "Carbon" in the bore after ignition will probably bond with the atmospheric oxygen in the bore at the sort of temperatures involved. There is, however, that other "greenhouse gas", water vapour, formed in all this high-temperature conversion from solid to gas. Not likely to stick around long in a warm barrel, however.
Think about the forces and temperatures at work when a cartridge fires and it makes sense.
Nickel bullet jackets certainly leave nasty "streaks" in barrels. Gilding metal (basically a soft brass) also leaves distinctly-coloured streaks. Leave that lot sit in a barrel that is regularly firing corrosively primed ammo, i.e. almost ALL surplus .303 ammo ever made, and the chloride salts from primer ignition will be embedded in layers in your bore. Hence the time-honoured trick with the boiling water and the nifty funnel.
Most modern bore cleaners will work, but it's not "a quick once-over" and done. If you are using "surplus" ammo, re-clean a couple of days later. (Also done with the "water-cleaned" rifles). The crud that "sweats" out of the bore over a couple of days is disturbing when first encountered.
Even chrome-lined barrels are subject to corrosion with ANY ammo, if not given correct attention.
The chrome lining is not some impervious miracle shield. It is basically there to reduce wear and erosion, not totally remove the need for cleaning. Hard chroming in barrels is utterly different from what is found on the "shiny bits" of classic cars. There is NO pre-plating with copper, for a start. Hard Chrome is formed on the steel substrate as tiny "nodules", and it actually looks "lumpy' under a microscope. However, this is actually part of the reason chrome lined barrels seem to be "slick" to bullets. The bullet is actually riding on the tops of these little nodules and thus has less surface contact and thus "drag". Back in my younger days of shooting the L1A1 in service and personal use, there was a quick way to tell if the barrel had a fully chromed chamber and bore, or, as in early ones, just a plated chamber. Run a loose patch, soaked in "Sweets" solvent through the barrel. Wait about a minute or so and then run a firm-fitting, clean dry patch through. The "standard" bore would show distinct blue streaks, indicating the removal of jacket fouling. The fully-chromed bores showed virtually NO colouration for the same amount of rounds fired.
The downside of this "slick lumpiness" is that there is micro-porosity between these nodules and that is where the corrosive molecules find their way to the steel substrate. The result is RUST underneath the chrome and the first thing people start to notice is "chunks' of chrome going missing, especially near the muzzle and back near the throat / leade. Furthermore, chrome lining works fairly poorly on conventional "square-cut" rifling. Sharp, external corners, such as on each side of a the lands, create a higher current density and thus greater chrome deposition. This tends to be fragile and gets bashed off by bullets traveling up the bore. The reverse occurs in the tiny corners at the bottom od the grooves, Poor deposition leads to greater risk of corrosion. That is why well-designed chrome-lined barrels have radiused corners on their rifling; see H&K style "polygonal" rifling for the idea. Ditto "5R' rifling.