The sounds hard
Doesn't feel hard to me. I have a bag for USB A, a bag for USB C, and a bag for USB A<->C.My USB-C charging cables are all 3' or longer, so they're visually distinct from the crappy little cables that come for free inside the package for various budget-priced gizmos.
My Thunderbolt/USB4 cables are labeled as such, and I am very confused that you are talking about Thunderbolt/USB4 cables so stiff that they cannot bend to fit into a container or bag.... I mean, mine are stiff but not that stiff. Plus these are expensive cables. Not sure I have any spares. Those are bought for purpose.
Charging is an interesting case, I actually deliberately use crappy cables for that too, depending on the charging time I need!
Re: stiffness: I mean I guess it depends, how big is your bag. I'm thinking like a freezer bag not a grocery bag. I could bend them to fit but then I'd probably mess them up.