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).
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.