When doing $1$-category theory, there are often no tangible advantages/disadvantages to drawing diagrams in one shape or another; for example, choosing to draw a naturality diagram for a natural transformation as a square as opposed to a trapezoid, or parallelogram, or circle, etc.

In $2$-dimensional category theory, the choices seem to become less arbitrary; there are diagrams which are 'easy to read' when written in some geometric configurations, and 'difficult to read' in others.

In $3$-dimensional category theory, diagram geometry becomes crucial for clear communication of ideas using diagrams; here the vertices are objects, edges are $1$-cells, faces are $2$-cells, and enclosed $3$-d regions are $3$-cells. (Unless you're working with string diagrams, then reverse the ordering.)

Has there been any work done on a 'systematic' way to 'correctly' write out diagrams in higher category theory?

It's usually possible to figure out a reasonably nice way to write a diagram through trial and error, but the larger the diagram in question (and the more dimensions in play) the longer this trial and error process typically takes. It would be nice if there was some systematic formula one could follow when drawing out higher dimensional diagrams, maximizing the chances of 'readability'. Any pointers are appreciated.