I already have three kinds of C to C cables, some that will work with my laptop+monitor and some that won't, then some power-only ones for random accessories. We can no-true-Scotsman all day but so far type C hasn't simplified my life and as far as I can tell it won't in the near future. iPhones switching for me will just mean throwing out a decade of Lightning cables and buying USB-C cables.
They are charge cables that come with random accessories, I think I bought some long ones as well. Also A to C cables. As long as they're only used for low-draw devices it should be safe but requires keeping track.
The vast majority of C to C "charge" cables are USB 2 cables. I don't believe I have ever received or even seen a "charge only" non-captive C to C cable. A to C cables are a lot more common.
Do you have reason to believe that the C to C cables you got/bought don't support USB 2?
It doesn't make sense for a random accessory to come with a charge only C to C cable because USB 2 C to C cables are a dime a dozen. They're almost certainly paying more money to produce a spec violating cable.
They could have data support, I've never actually checked. The wires are pretty thin so I only trust them for charging the lights they came with. I have a bundle of similar looking A to mini or micro B cables of which I know many are charge-only. As long as they're super short I only rely on them being useful for charging.
In that case they almost certainly do have data support.
Keep in mind that power dissipation scales with the square of the current. That means that, as a first order approximation, relative to household 15 amp wiring, a 3 amp cable can be 1/25 of the size. You can get away with really thin wires for that.
The reason why you end up with thick USB C cables is because of either 5 amp support (requiring 2.8x bigger wires) and/or USB 3 support (requiring a bunch of extra higher spec wires). It is quite normal for plain old 3 amp USB 2 USB C cables to be thin.
I'm curious, next time I'm charging devices I'll check. Either way they're still not useful for anything beyond accessory charging, they're short and won't carry the power+signal necessary for my laptop (which, sigh, has two kinds of cables because the one Apple provided with their charger won't do Thunderbolt).
The minimal spec C to C cable is USB 2 data and supports power delivery with currents up to 3 amps (i.e. 60 W at 20V 3A)
This is enough for most phones, and almost all of the exceptions use proprietary charging that isn't going to work on a C to C cable anyway.
The labeling issue of all these cheap shit cables is a serious problem, but it is a nonissue in the phone charging context.