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> > I cannot make sense of a board cutout as a layer. It’s an
> > operation that applies to a set of layers.

You're confusing drawing layers with physical layers.  PCB's drawing
layers are just collections of shapes, much like gschem's "schematics"
are just pages of lines.  How each layer is interpreted depends on
what the people at the fab house are expecting.  If you tell them "the
shape in this gerber is for internal cutouts", that drawing layer then
means "shapes for internal cutouts".

> Neither do I. The drawn shape is either a positive image or a cutout.

It's just a shape.  Interpreting it is up to the humans who talk to
each other about what the shapes mean.  It would be nice if there were
automatic ways of conveying this information (perhaps STEP) but at the
moment we're relying on good old "talking" to solve that problem.

> Gerber file format have the concept of dark and clear polarity.

Irrelevent here, though.  And I've seen way too many fabs get this
wrong; pcb never takes advantage of this.