I’m 100% sure if some sort of tournament requiring wood existed, it would get nerfed too. They won’t do anything RE: wood because people already have tens of millions saved in the form of battle items. I suspect it’s also why there’s no rush to open the rest of the town. People would only have to sell their items and wait for the build times to finish and they’d be maxed out with little to no effort, and there’s no money in it.
I wouldn’t be surprised if upon the expansion of the town, a new game currency comes along with it. Iron/steel would make sense, and force people to start from scratch.