Wow I finally figured out what the edge split modifier actually does, though I have been using it for some time 🙂

And this is a bit stupid because it does what it says it does: it splits, separating faces and duplicating vertices. The use I had found for it (spotted in a tutorial) was applying smoothness to a complex object while keeping some sharp edges. The smooth and flat functions (in mesh tools) are rather crude. In edit mode you can apply smoothness to just sets of selected faces but there are objects you won’t be able to pull off like this.

One example is this extruded weird shape:

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