Lossy compression for alpha channel isn't that good idea, I think. Brightness and color compression artefacts will be multiplied by alpha compression artefacts.

Then provide baseline support for an uncompressed alpha channel. Not being able to store one at all in an image limits the usefulness of the format.

Artifacts for lossy alpha compression are already, to some extent, well understood and dealt with, since compressing video game textures that contain an alpha channel is already done lossily using the DXTC compression formats.

You could choose alpha compression quality separately from luma/chroma. Alternatively, either compress the premultiplied colour values directly, or compress raw colour but optimise the premultiplied error.