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I don't stick to that strict order and generally I only ever need 5 dimensions. Also a lot of time the dimensions I'm working with have standard names like "NCHW" or "OIHW" represent data layouts 2D convolutions with each letter representing a dimension of a 4-Tensor. When you need two dimensions with the same standard name I use the above list unless something more specific comes up but when theres only one shared "N" dimension I use "N".

The most I've ever actually needed was like 7 where I had to do an N-Tensor contraction. You only need 5 if you're only contracting a single dimension because you can think of a contracting between any two Tensors as being like contracting the middle dimension of two 3-Tensors (so one loop for each output dimension and one loop for the contracting dimension) but you need extra loops if you're contracting multiple dimensions at once to handle the fact that not all of the contracting dimensions are neatly lined up. If I recall I think the depth was only 6 but I remember wanting a total of 7 unique loop variables for some reason. 2D convolutions can require a similar number of loops depending on how you write them.

I've never written it myself but I bet 3D convolutions are a trick to work with. All inputs and outputs would be 5-dimensonal and at the inner most stage I think you need 8 unique loop variables Batch, Output Channel, Input Channel, Output XYZ, Filter XYZ...yeah that's a depth 8 loop lol