High Current PCB Design (polygon pour vs thick tracing)
Copper pours should work fine. You can estimate the resistance of a track with an online tool, for a pour it works the same. Make sure it is not cut too much by tracks which would reduce its width.
If your USB connectors are surface mount, you will need vias to connect your USB's to the bottom layer and these have resistance too. So you need to check the copper plating thickness in the vias from your pcb fab. It's not pure copper, rather copper deposited by electroplating in a bath, so it has higher resistance. Check this calculator.
Also if a short develops at the end of a 5V 2A USB cable, or worse a 5V 500mA cable, it may not draw enough current to trip the 18A current limit in the supply. In this case the short will produce a lot of heat, which could melt the insulation, or start a fire. If the short occurs inside the device side USB connector of the cable it will heat up and melt or ruin the device's connector.
So it would be a good idea to add a 2A current limit for each outlet. There are USB power distribution chips that provide this functionality. A cheaper option is to use a polyswitch (PTC self resettable fuse) on each output.