Features shouldn't be there 'just because it's possible', at least not if they may impact other features(1). If greater compression can be reached by leaving out the alpha, and if there's no compelling reason to put it in, it should be left out. 'why not' is not a reason, there needs to be a business case for each feature, in everything.

In my experience, and this seems to be a widely held position, the main use case for jpgs is in pictures, as in photographs. The main use case for png (gif) is for graphical elements: borders, menus, etc. Those last ones you want to compress with a lossless format anyway - you need to be sure that a flat menu background is not dithered or doesn't have other artifacts. I understand the question mostly as 'do you need transparency in photographs' and 'do you need non-rectangular photographs where the non-rectangular nature is encoded in the photograph itself, and not part of another rendering in stage in the presentation layer'.

Thinking about it more, maybe things like drop shadows or other fancy borders could be case where you need transparency in photos. Otherwise you have to work around it by having the picture as jpg and the border as a separate (or several separate) png's. More requests, harder layouting, etc. I'm not convinced yet that this use case alone is a compelling argument.

As for technical reasons to not implement it, I don't know - I'm assuming there are because I'm quite sure that someone at Google must've thought about it and decided against it, they must have had their reasons.

(1) I'm reasoning from the assumption that including transparency has adverse effects on file size and/or decompression complexity. Maybe there aren't in which case balancing features becomes a different matter and most of my argument is moot.