Take this feature request with a grain of salt: I han't seen other illustration applications do this, so I haven't tried it.
I was working on two things that made me think about this feature:
1. A game UI
2. A game texture that requires tiling
The feature consists of this: In addition to copying a layer, you can Copy linked layer. What this does is create a copy of the layer that stays in sync with the geometry of the source layer. Adding, editing and removing nodes on any of the layers also adds them to the linked layers.
In the Linked layer, besides the on/off checkbox there is a Link styles icon, off by default. If it's on, gradient, line style and Layer Styles are kept in sync between layers.
This allows this to happen:
1. While working on UI, you may need multiple shadows, gradients, in a single piece of geometry. Other vector software does this by supporting multiple styles per layer. With this system, you add a linked layer with "Link styles" off. You can add the new styles to the linked layer.
Advantages (over multiple styles per layer): Because a linked layer is a layer, you have more flexibility: you can add a mask to the linked layer to apply the style in just a portion of the object. You can also choose the order that the styles are stacked by reordering the linked layers. It may be easier to achieve some effects because you can just offset a linked layer to apply the style with an offset.
Disadvantages (from multiple styles per layer): Moving or rotating the source layer doesn't move the linked layer, so moving and rotating is less convenient for the "multiple styles for one geometry" use case.
2. A common activity is to create shading on an object. However, keeping the shading in sync with the base layer is difficult if you edit the nodes in the base object. With linked layers you can:
1. Create a linked layer ("Linked styles" off), this will be the "shading" layer.
2. Change the linked layer's (shading layer) gradient to the desired shading.
3. Create a mask for the unshaded areas on top of the linked layer. Mask to Below.
Now, if you edit the base object, the shading layer is updated to match its geometry.
3. While working on a tileable texture, copy linked layers to the 4 corners of a source layer, with "Link styles" on. Now the source layer is replicated to the 4 corners, so you can see if it tiles well.
1. When you "Copy linked layer", all styles and geometry of the source layer are copied into the linked layer. For use case (1), it is probably useful to have another feature: "Clear styles" on a layer to make it easier to delete all styles on a layer and add new ones.
2. Linked styles is off by default.
3. It sounds useful to be able to Link groups, but optional if it's too complex.
4. Since CMD+J copies layers, sounds like CMD+OPT+J should copy linked.
This is just an idea to implement some useful use cases (some of which I may not have thought of). Of course, feature bloat is bad, so if this turns out to be a bad idea it's better to not have it so of course criticism is welcomed.