I'm also wondering about things like (APL-style) inner products -- they are undeniably powerful, but it's hard for me to conceptual use cases above rank 3.
In my code I'd sometimes write assertions in the beginning of a function to not only ensure it's called with the right shape but also as documentation.
Also, in practice really high rank arrays aren't used much. Even 4 is pretty rare.
I basically never use the generalized inner product; it's rather unique to the original APL - J has a variant that doesn't have the built-in reduction, and k and BQN and many if not most other array languages don't have any builtin for it at all. And in general I don't typically use rank higher than like one plus the natural dimensionality of the operation/data in question.
The best analogy i can give of my thought process is that first i unfolded the problem into one or more many-dimension object(s) ... then took a different "stance" of looking at the object, then refolded them into the final solution.
So yes... I had it all in my head at some point.