I find myself copying a lot of work as well. Copying is more useful to me than tutorials because it really forces you to look at something with a lot of attention to detail. Often, we THINK we're looking at something and learning from it, but we're really mostly consuming passively. Copying forces you to consider all the elements and concepts that went into a piece of work. Like Victoria said, you're more attune to spacing and proportion, etc...

Aside from copying, I find myself doing a lot of intentional experiments where I give myself certain constraints to work under. So maybe I decide I need to use a certain tool, or I have to render a subject in a different style than I'm used to.

Imo, getting better at visual design is mostly about sensitizing yourself to details that most people take for granted. Any activity that forces you to look hard at something can be a great learning experience. Contour drawing, life sketching, etc... The subject matter isn't at all important – your attention to detail is.