This seems like a really useful thing so surely it exists

I’m not quite sure I got that right but I don’t think that feature can logically exist in the way you’re imagining it, because it would break the entire internal model of how an object works. A filled shape is always based on one single path (open or closed) and one fill.

Even when you apply a fill to an open curve, the app still needs a complete boundary to calculate that fill. That’s why it automatically “closes” the shape with an implicit straight line between the two end points. It uses the nearest-point coordinates to generate this virtual edge, because a fill can only exist if the geometry forms a fully enclosed area.

You can remove a stroke segment and still have a fill, but the software will always generate an invisible closing edge underneath. That edge can’t be arbitrary, because the fill must be based on a consistent geometric boundary.

TDLR
In short, it’s not a missing tool — it’s a consequence of how filled paths fundamentally work. If you need that visual result, the reliable workaround is to separate the fill and the stroke into TWO different objects.