It's a really big deal that the WoL was able to be brought across the rift with their physical body intact - not even the Ascians can do that. They just abandon their host and pick up a new one in the other shard when they arrive.
The Warriors are either possessing corpses like the Ascians do, or more likely are "solid aetherial ghosts" like the Scions in the First. They had to kill their original bodies exactly because they couldn't be transported across, and the souls needed to be freed to travel.