Cartridge loops are most definately not a Hollywood product, unless Hollywood was a post saddler on western military posts in the 1860's. Ordinary soldiers were also sewing loops on their belts in that period. Cartridge loops were becoming common in the mid-late 1860's. Regular military pistol belts were being modified with loops by several saddlers for rifle cartridges, and later pistol cartridges. So much so, that the Army, before long, began making them for issue, and abandonded the cartridge boxes in use before then.
If you want to know what was used back in the day, dig up a copy of "Packing Iron", it has some excellent historical information about gunleather, and some very good pictures of period gear.
I store rounds in my belts, and have for probably 30 years. It hasn't caused any true trouble, just the minor annoyance of the verdegris. I like having them ready to go, so consider it a worthwhile tradeoff. I use a plastic bore brush of a smaller size to clean the crud out of the loops carefully, maybe once or twice a year depending on the belt, and clean the rounds off now and then before heading out into the hills. I've started using some nickel plated brass in some calibers to eliminate the crud issue. The Army used some tin plated cases in the 1880's I believe, just for this reason, but went to canvas belts and dropped the tin plated cases. I also like the nickel brass for another reason. I only load bear loads in nickel brass in 45-70 and 45 Colt, so I know at a glance what the load is when checking a belt or gun when heading out.