Motion path not showing in Shape Layer Groups

The only motion paths that show up in the Composition panel come from the Layer/Transform/Position keyframes. If you separate dimensions as you have done in the screenshots, the Bezier handles on motion paths disappear, and it is impossible to control any curve or acceleration on the motion path. 

The screenshots do not show any Illustrator files. There is no reason to convert vector layers (Illustrator files) to Shape layers unless you want to extrude the layers using the C4D rendering engine, use Shape Layer animators like Trim Paths, convert the shape layer path to a motion path, use the Create the Nulls from Paths script file to trace a path, animate a path, or use the nulls to animate a path or convert a vector path to a motion path. Converting complex AI files to shape layers also causes problems with gradients, brushes, and other effects applied in Illustrator. Render time also increases if you convert a vector path to a shape layer. 

Shape layers cannot be opened in the Layer panel, so You cannot use the view options in the Layer panel to see and adjust motion paths from effects, the Anchor Point, or use the other tools available to other layers. Vector layers to Shape layers. 

If you really need to see and control or edit the motion paths in the Composition Panel for individual shapes, you have to create those motion paths on another layer using a null or a shape layer and then copy and paste it to or use an expression to attach the movement to the Contents/Shape/Transform Shape/Position property. 

I'm not sure what your design goals are. I hope this helps you understand the workflow. I use complex, carefully prepared Illustrator files all the time, but if I need to convert any of the layers to shape layers, they are always simplified objects with no gradients, effects, or brush strokes applied to any objects in the layer. Most of the time, there is only one path on the layer I am going to convert, and the layers that are going to be converted are often simplified copies of another layer in the AI file that I need to reveal or use as a motion path.

I hope this helps you figure out a workflow that helps with your project. Maybe someday, the User Guide for After Effects will include a more detailed explanation of the reasons you would need to convert AI layers to Shape Layers.

I hesitate to point out this alternate workflow, but if you really need access to every element in an Illustrator file, every path, gradient, and brush, you can Install XD on your system, start a new project file, Import an Illustrator file to XD, then before you do anything else, use the File menu to Export the project to After Effects. You will end up with every part of the AI file as a separate layer or nested comp (pre-comp) with the vectors intact. Complex AI files can easily end up with hundreds of layers in the entire comp structure, but it is the only way to get access to every property in an AI file.