People have asked for all sorts of things for that screen, mostly without remembering that that screen is, by definition, used by people who aren't really awake yet. We've also had complaints that that screen is too complicated already for someone just waking up, and anything that requires any sort of comprehension is going to fail. We've had to enlarge and move the two existing buttons a couple of times already.
Frankly there's no right answer that works for everyone, which is why we added the ability for developers to customize it.
Since the above post was written, you can now quickly resume the music the alarm used by going to the Music screen and hitting "play".
Also, the above-mentioned documentation is currently on the wiki here.