When it comes to the alpha-channel I simply just find it as useless as multiple cores. Ordinary RGB is and will always be good enough.
Alpha is used in images for compositing.
Consider it this way. A Game, or other piece of software, that has a customizable background. The software or game has a title screen, and they want it to have a "drop shadow" on the text. This means they either draw that drop shadow manually in the source code (consuming extra CPU time) make a separate image for every single possible background image, or simply use an extra translucency channel on another image. This let's the same optimized blitting code to be used to blit the new image and composite it over the original, creating a new image. Another important thing is that a lot of programs generate full, 32-bit bitmaps on the fly for various purposes for compositing. usually in a layered approach: for example, when a given object changes shape, the program might create a translucent drop shadow image, and cache that for later use. Then when it does use it, it might create the composited version (with the normal image and the "drop shadow" image, with the former drawn on top of the latter) and cache that for drawing purposes.
For the purpose of actual display, 24-bit RGB is usually plenty. but when <creating> that 24-bit RGB image to be shown on-screen, Alpha can be used to composite various images to save both CPU time as well as disk or memory space. Without sacrificing appearance.
But even then: 24-Bit RGB isn't enough for everything, since the color space literally cannot show every single possible colour. This is, as I noted earlier, particularly prevalent with the purposes of desktop publishing or printing, both because of the different color space but also because sRGB cannot represent certain tones and colours with 100% accuracy, which can result in the output in a screen looking different on a printer. This of course is partially unavoidable, since screens are likely to use RGB colorspaces for the foreseeable future- but locking the images themselves to use the RGB Colorspace can be a problem in these cases because the original information is lost in the conversion to the colour space.
I have tried to find a single situation that transparency really is needed, but I can't find any.
And you've accused us of not having imagination... It's translucency, really; but 1-bit transparency masks are useful too, for many of the same reasons. If it wasn't for transparency masks and transluscency, every single icon used in today's GUI systems would have the same color background.