If I'm understanding this correctly, your saying a 20w power supply connected to a device with a 20w rated SOC, wouldn't allow it to actually pull 20w, but would only be able to pull 16w due to 80% efficiency? That is mostly incorrect. You have the efficiency portion of it correct though.
In the case of Switch, if you have a power supply that is rated for 20w, that means it will be able to output 20w of DC power max. DC is what electronics use. Now since power supplies are not 100% efficient, and the best you can get is around 80%, what that actually means is that the 20w power supply, has an input rating of 25w AC. The power lines and all buldings have AC power (I know some have DC but its so new and minuscule lets not cause confusion)
This is due to the law of conservation, and the first law of thermodynamics. When AC power from the wall is transformed into DC power for the electronic device, there are some energy losses in the form of heat. This is why power supplies used to run so much hotter than they do now. Old power supplies used to be around 50% efficient, so a large amount of heat was created. Todays power supplies are around 80%, and sometimes higher, which create much less heat.
Now for the battery, if the DC voltage of the battery doesn't match the voltage of some of the electronics in the device, then it needs to be converted, but DC to DC is done quite differently than AC to DC, and to make it short, the amount of loss you get with a DC to DC conversion is quite minimal. This of course is all calculated when designing the system, so supplying enough power, whether through the power supply or battery, will feed the device properly with whatever it requires.
If I'm way off base, and this isn't what you meant, I apologize in advance.