[Silhouette]

Given these two possibilities, why would one choose to place switches in disparate places throughout your code?

You are touching on something called the "expression problem". You might be interested in reading some commentary about it. There is an inherent decision to be made any time you have many algorithms each operating on many data types. In most programming models, you have to choose between grouping your code based on your data types (but then any new algorithm needs to be implemented on each data type) or based on your algorithms (but then any new data type needs to be supported by a new case in each algorithm). Neither is the "right answer". You fundamentally have a two-dimensional system here, and you need to decide which axis you are going to prioritise in your design.

[bendbro]

Thanks. I will look into this. I would like to see examples that obviously require algorithm-grouping or type-grouping, as in my experience, algorithm-grouping has always lead to headaches.

I think I have encountered this issue in the past but was turned of by the lack of formality in the discussion. I wish there was more academic, concrete discussion of these issues, because I feel that what I am doing now (informal discussion) likely has many holes.