It would be nice to be able to create a shape that has different edges between different points. At the moment, the closest that you can get with this is the width tool or by deleting a segment (which causes a host of issues, since it would no longer be a shape).

More broadly, by isolating line segments as editable aspects of a shape, it would be great to be able to apply edge effects (feathering, roughen, blur, etc.) only to a select number of segments on a shape.

This would give finer control over shapes in Adobe Illustrator and make it possible to create more dynamic, detailed illustrations.