No one explains it this way for some reason, but USB-C "60W" is more like USB-C
20V. All USB C-to-C cables are supposed to be rated to something like 600V by laws and common sense, and 3A by USB-C spec. 20V x 3A = 60W.
USB-C in C-to-C configurations require all the PD pins working for voltages to be supplied at all. So all USB-C cables that aren't the ones that actually don't work at all should be able to do that 20V x 3A -> 60W. Only in rare cases where a C-C cable is wired to make it look like one by being internally wired as C-A-A-C it becomes problematic since only USB-C has the config pins used for non-5V modes, but that should be actually rare.
I think USB-C shaped thing mentioned in GP refers to USB-C devices, like dollar store Bluetooth speakers and such. For those things, it's in fact not so rare that they come with tons of stupid quirks.
The can of worms is mainly in USB 3.0, Alt Mode, 5A mode, and Thunderbolt/USB4. 3A mode is fine. Raspberry Pi notoriously used a "5V 5A" mode that it's not supposed to be using.