I like the idea a lot! We could 1) allow clicking edges to add a vertex while the mesh trace dialog is open, and 2) add a button to allow you to apply only the "refinement" part of the mesh tracing:
Tracing currently doesn't have the concept of moving the vertices closer, instead the refinement step moves the vertices to make the mesh have a smaller area. If this is what we do when the
Refine button is clicked, it may not always move the vertices quite like you want. We've added it in 4.1.10-beta, maybe you can give it a try when it's released?