A better use for timber would be building the structure of GF4 out of wood. There is a big global move in building towards mass timber construction as it has much less embodied energy and can also be built quickly. Glu lam beams for the main structure and cross laminated timber for suspended slabs. Wood like spruce is typically used but they should also be able to use pine, although drying may be an issue for anything harvested on site.
Oslo airport is a nice example of what's possible with timber: