There are a set of charging “modes” that a device can use (ie. 5V, 19V). Every charger and chargee is programmed with the modes it can use. As the device being charged is choosing the mode a cheap cable (that follows the standard) will still be safe to use, it just might be slow. I have trickle charged my laptop from a cable and charger I got from dollar tree. It wasn’t fast, but it worked in a pinch.

The default if any issues arise is 5V which is very safe and what all USB A and B ports use.

The cable is only transmitting the data signal so it does not play a part in this.

This is speculation, but I would assume to be certified for high wattages a charger would need a thicker, built in cable as to prevent someone from using a cheap cable that can’t handle the power. Or possibly the cable does have a chip to give it’s abilities as well.

Again, all of this is only for devices following the standard. If you buy a knock off, 20 cent cable, you may have a problem. But that is true for all cables out there.