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…
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.
