Sure, but then you're doubling the total
power wiring required and also making each individual
fixture more complex & expensive. It's much simpler to have the emergency fixtures get
power from a single normal/emergency feed, and put all the complexity of deciding when an emergency is happening into one device rather than replicating it across many fixtures.
Also, your exact approach describes a transfer between normal and emergency power--which means each
fixture needs to be UL1008 listed instead of UL924. That would add even more expense that could be avoided if the fixtures are always powered from the emergency feed and just use the normal feed for sensing a
power failure (instead of actually transferring between normal and emergency
power). At that
point, though, you're most of the way back to my suggestion, except you still have more expensive fixtures and an extra run of normal
power to each of them.