Somewhat this. However, I am sometimes reminded by my more creative minded friends to abandon the rigid developer mentality of 'commit and keep everything ever; just in case' and instead follow a more creative focus on just making something. I have practically found that exploring too many ideas and branches ultimately delays the completion of any creative process ;)
What if the tool does the committing, and automatically does the commits as deltas? Something like the idea that the 'save' is fairly similar to the undo-redo data rather than some optimized object graph or optimized relational database representing one iteration.
I use Git on my Reaper projects all the time. But I've almost never gone back to an earlier version, and when I have I could've probably anticipated the branch point and just used "Save As". Nonetheless, it feels nice to have history "just in case".
If it does this for multiple authors, then it would be invaluable for cases where different composers are handling different aspects (such as if one composer is focusing on percussion and another is focusing on wind instruments, as is sometimes the case when composing music for marching groups).
Doing what you suggest would require closing and re-opening the project (which can take a while when working with GBs of samples).
Moving through the version tree could be as fast and efficient as undo/redo operations, which are usually instantaneous. In fact, DAWs already implement version control! It's just ridiculously limited, since all you can do is undo/redo. Depending on how they manage it internally, adding better version control features might not be that difficult. History and snapshots (a la Photoshop) would already be a vast improvement over what's generally available in DAWs.
There's a LOT of binaries involved (in the sense of large .wav files at least), and I doubt the Live file format particularly lends itself to text-based version control
The Live file format is gzipped XML. It very much lends itself to text-based version control. (I've even played around with adding such as a third party.)