Shape Keys should deform UV positions

Very useful for eg. Pupil dilation in eyes as well as the most useful technique to do a 2D face like Animal Crossing. Since shape keys and bone deformation is the only things you can animate and transfer with .fbx as export to a game engine, this would be a great help.

Shape Keys are just liniear interpolation between mesh data, whether it is UV or Vertex position shouldn't matter.

Houdini can do this and it used to be a feature in Maya too, until they "fixed it" as a bug despite it being used extensively in rigs everywhere.