I doubt the users find the app pointless, but there isn't much reason to steal someone's account. You can't even link it to their real name to blackmail them.
As a high schooler surrounded by a lot of Yik Yak users, the real value I see people finding from this exploit is the ability to associate multiple posts to a single user, allowing you to make connections and potentially find their identity. A lot of people I know also selectively tell people about some of their Yaks, so with one Yak you can find the rest.
Sorry, I'm really ignorant about these things, but once you have the ip of the phone that sent some message, couldn't you trace that to the physical phone? So you want to know who posted "foobar", you wait until you have someone's user id that posted "foobar", and then use the IP address of the most recent outgoing message to identify the phone. Since there's typically one user per phone, won't that identify the user?
Knowing the IP is pretty useless. The closest you can get publicly if you know that is the general region, but this app is already a nearby radius app, so you already know that. If you have law enforcement powers you can try to get the subscriber info who was using that IP during that time period, but normal people don't have that ability.
Even the article has to fall back to saying you have to just keep monitoring packets with that IP and hope the user uses some non-HTTPS web site that reveals their name. Although, honestly, most ISPs don't give you a static IP any more so the same user could be a different IP address multiple times a day.
As demonstrated in the article, this gives you a local IP address which you could use to find the hostname of the device. For iOS devices, the hostname often contains the owner's name.
Deploy the hack on the local network and grab the ID of every user. Then check each ID to see if they made that post. Of course, this requires either foresight or for Edward to keep posting afterwards, but neither is outlandish.