Thirding the desire for an all-fabric Double Organizer Pouch.
Similar here. I carry a COW every day because I love them, but I only keep non-wallet-standard items in the clear section (barrettes, hair tie, toothpick, occasional pills) because I don't like having my ID visible whenever I pull out my wallet. I've tried keeping a Metrocard or train tickets in the clear plastic section, but since that section is more grippy by design, as you point out, it's just not convenient for sliding things out quickly, especially while still inside your pocket.
I've gone to buy DOPs a number of times but stopped because I'd forgotten there's no all-fabric option.
I'd also love a Pen/Pencil size all-fabric DOP.