What is code or common rule when securing multiple electrical lines?
Bunching together is a serious issue.  For instance, in EMT conduit, you are allowed only 9 active conductors regardless of pipe size, unless you derate (use larger wire than normal).  That means four circuits, or three 3-phase circuits.  I notice the multi-cable racks only hold 4 cables.

The reason is heat, and you have to design for worst case, you can't armwave it with "it's residential, they'll never all be used at capacity at once." At least it isn't for you to armwave; Code decides which corners may be cut based on a lot of research and experience.  Even then, Code is a bare minimum- common sense also applies. I wish a Code expert would speak up.