It saves having to go through the Suez Canal. It's always a good idea to have alternative routes, it keeps costs lower. Also, Turkey (regardless of who is in charge in the Turkish parliament) wants peace to break out all over the Middle East. It would help business for Turkey (which is already decent), by opening up stable markets outside of its European neighbors. Also, it could very well help Turkey (and perhaps Israel) enter the EU at long last.
I forgot about Elat and didn't zoom in enough to see it.
Thanks!