I'd love for the pathfinder to be able to cut up bitmaps, avoiding having so many extraneous paths in a complex file
It would be nice if I could embed a jpeg or some other graphic format and then be able to use the pathfinder tools to change the shape of the image. Seems doable as the graphic imports as a path that happens to be filled with pixels rather than a color or pattern. The main reason I'd rather use the pathfinder for this over a clipping path is to reduce the number of paths in a complex document. When there are many elements in a file, having a lot of clipping paths makes the structure of the file difficult to parse due to the use of paths that have no stroke or fill.
Egor Chistyakov commented
Jody, there's a way to make it work, but with a different method.
Create a rectangle, fill it with white, set it to Multiply blending mode, select both image and rectangle and apply Flatten Transparency with the settings from the GIF attached.
But yes, what you want makes sense.