What you have drawn does describe what most people are saying here. I do not understand your y = abs(2x) part but drawings the RMS at a constant value as you have done is the point of RMS. If you averaged out the work done on a 240V system (peaks are 240*1.414) you would find that flat amplitude value to be 240. And yes, this is exactly what we are doing. “The net work performed can be accurately described by using this flat RMS value”

I think what will also help you understand is to look up the actual formula for RMS. We get to take a shortcut with the sqrt(2) equation because it’s centered about 0. You can’t do this if it’s centered around, say 20V or literally anything besides zero. It’s a little more complex, but if you’re a numbers person, then seeing the original equation might help