There has been lots and lots and lots of attempts to replace steel with wood in construction. These attempts have gone nowhere. So what is to say that this time it will be different? If wood is so good for tall construction why isn't it already used in skyscrapers?
The best thing in their favour is how standardized and simple a wind turbine tower is. They know the requirements and their customers. It's much easier than a skyscraper, and it might let them start to scale production of the materials so they become more attractive to other applications.
However there is growth in mass timber construction generally. People are competing to build taller and taller timber skyscrapers.
Most traditional constructions in Asia (and to be frank anywhere else in the world) has been with wood, stone and dirt. Steel is only possible since we extract enough iron and burn in with coal, something we're not sure to be able to do at the same price (=rate =quantity) as we did for the last 100years. Still, here's some contemporary "skyscraper":
