It is worth noting that register coalescing gets a lot of attention in interference graph coloring allocators because they typically have a pre-pass that inserts copies everywhere (because adding copies or spills later is so hard). So instead of worrying about where to insert copies and spills, those allocators worry about what to coalesce instead.

In my own compiler (where I don't add copies in a prepass) I have not yet found a case where any coalescing would be beneficial.