Not textures, but line stipple would be marvelous to be able to add to edges. Vector textures for faces that results in crisp vector export from LO would too be very useful. And these vector textures used as hatches on section fills would take that feature to a whole new level. This is what I’d like to see in SU2019, 2020 and 2021.
I don’t think adding textures to edges causes any problems, except that you maybe are annoyed by having invisible noise in the model. I actually didn’t know materials were assigned to edges when edges aren’t set to be colored by material in styles. It would make sense if painting edges was only possible when edge color is displayed, similarly to how hidden geometry display affects how faces/surfaces are selected with selected tool.