The most obvious application I can think of for reversing bits within a byte would be for image processing applications, such as mirroring an image horizontally, or making kaleidoscopes. There are probably signal processing applications, too...
...but only a 2-color image.
Separate bitplanes were very annoying in many respects, and the demise of the approach was probably regretted by only a few. But storing each bitplane separately does have one major advantage: you can just write all your algorithms to operate on 1-bit images, and they automatically run at any bit depth. Just run the routine once for each bitplane you're interested in processing.
(That may also mean the hardware is simpler to implement - one plausible excuse for its ubiquity. Not my field of expertise though...)