But at no point, either in the CRT or in the human eye, do the ringing artifacts actually show up. So any pipeline that renders those when you blow the pixel up is worse than rendering just a giant square.
They do. If you try to draw a white pixel in the middle of a black background on a CRT, the white bleeds around in a small circle, and if look at a point light source in a totally dark room, you will see a small halo around it. These are both ringing artifacts.
You see faint light around the pixel/light source. You don't see the edges of the pixel/light source as brighter than the center. Do you? (Can't check right now but it's not how I remember seeing things)