Yes. Focusing by moving the image plane is physically possible, and it has been used.

A well-known example is the Contax AX film SLR, which moved the film plane to autofocus even with manual-focus Contax/Yashica-mount lenses. View cameras also commonly focus by moving the rear standard (the film/sensor side) or the front standard (the lens side), rather than by moving lens elements inside the lens.

The main limitation is range and practicality. Modern interchangeable lenses often need complex internal movement of one or more optical groups to focus properly across their full focus and zoom ranges. Moving only the sensor/film plane usually gives less focusing latitude than moving lens elements, so it may not work well for all lens designs or all distances.

A possible advantage is that the optical relationships inside the lens stay unchanged, which can help preserve the lens’s aberration correction. In some close-up setups, moving the rear standard instead of the lens can also keep magnification more consistent.

So: yes, it’s possible; yes, it has been done; but for most modern cameras and lenses, moving lens elements is generally the more flexible solution.