> Would it be useful to consider “coordinative complexity” a separate type that's intermediary on the essential–accidental axis but also has other properties?

The complexity of getting different pieces to talk to each other? I can see how that's only conditionally "essential" in that, if you have enough control over the environment, you can make the various distributed components as similar as possible, never deal with version skew, and never deal with varying interpretations of the same protocol standard.

OTOH, if you're writing a web page, and you have to make that page useful across multiple browser types and versions, some way of dealing with the vagaries of different browser implementations becomes an essential complexity: You either push it into a library or framework or you handle it in the main codebase, but something has to know what MSIE can and cannot handle.