While reading this article, it struck me that the amount of "useless" data increases as the alpha value approaches 0. For example: in a pixel with rgba values of (1.0, 0.4, 0.5, 0.0), the rgb values are redundant. Is there a color format that would prevent this redundancy? Perhaps by some clever equation that incorporates the alpha values into the rgb values? I don't think Premultiplied alpha would work, because you still need to store the alpha value for compositing later...
Would you count compression schemes as valid answers to your question, or are you asking about the raw data not having any redundancy?
There're no channel formats or clever equations I'm aware of that avoids the redundancy part. But your question totally reminds me of Greg Ward's RGBE format, which is a high-dynamic range format stored in 8 bits per channel, with an extra 8 bit exponent channel. http://www.graphics.cornell.edu/~bjw/rgbe.html
RGBE isn't doing exactly what you're asking about, but it's similar in a way. Instead of storing 16 bits per channel separately for each channel, what you really get instead is 16 bits (sort-of) for the brightest channel, and the other 2 channels in 8 bits each - discarding the extra bits. You can't see them because the bright channel will prevent you from seeing anything super dark in another channel, so you can discard the extra color resolution in the darker channels.
If you count compression, then pre-multiplying would help the situation. Anytime the alpha value gets low or goes to 0, the color channels do too, so run length encoding or DCT or whatever else will collapse large transparent areas into all zeroes.
PNG uses compression to reduce the redundancy. The average number of bits per pixel is much less than 32. A=0 is a special case, and many PNG encoders will take advantage of that by setting RGB to some constant so it compresses better.
In premultiplied alpha, you can think of all the legal (non-emissive) colors as a triangle. At an alpha of 1, all colors are legal, tapering off as alpha decreases until you reach an alpha of 0, where no colors are legal. To turn the triangle into a square, you could scale it up by two, cut off the top, and rotate the top over into the empty space (like this: https://i.imgur.com/6hjNe7X.png). That would give you twice the colors you had before.
