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.)
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.