The back of an envelope is blank, and the front of an envelope doesn't need to be saved.
People may write on the back of an envelope because they're in a hurry and can't find a clean sheet of paper. Or they may do it because they are frugal and don't want to waste a piece of paper on a scribbled note that will be read and immediately thrown out.
I literally do leave notes for my wife on the backs of envelopes (and vice versa).
There is saying, "a back-of-the-envelope calculation," meaning a piece of arithmetic that's too complicated to do in your head, but just a quick, rough calculation.
Another similar saying--which also really happens--is "to make a sketch on a napkin." The real-life scene is that you are at a restaurant with friends, and suddenly you need to sketch something in order to explain it, so you use a (paper!) napkin to draw on.