No digital oscilloscope could ever reach the graph quality of an analog oscilloscope. Like no compact disc could ever reach the sound quality of a vinyl disk.
Vinyl sounds "beautiful" because we do like its distortion. Exactly the same happens with analog tape recorders. I don't have anything against purposefully introduced distortion, but that's what it is.
Now you can buy emulations of analog gear in order to "spice" your digital recordings or "add warmth". Guess what do they do? Yes, add distortion
There's nothing wrong with it. It's just part of the creative process. But those "magical" misconceptions about sound recording won't help you. Really!
So, what happens with an analog oscilloscope? It's been explained countless times. Analog scopes naturally display an average of many sweeps.