Reducing the embodied emissions of materials for new construction and renovation of buildings is a key challenge for climate change mitigation around the world. However, as simply reducing emissions is not sufficient to meet the climate targets, using bio-based materials seems the only feasible choice as it permits carbon storage in buildings. Various studies have shown that bio-based materials allow turning overall life cycle impacts negative, therefore, having a cooling effect on the climate. In recent years, scholars and policy makers have focused almost exclusively on the advancement of wooden buildings. Timber structures stand out as they can be prefabricated and used for high-rise buildings. Yet, one important aspect seems to be overlooked: the consideration of supply and demand. Large forest areas that allow sustainable sourcing of woody biomass only exist in the Northern hemisphere, notably in North America and Europe. In these regions, though, urbanization rates are mostly stagnating, meaning new construction rates are low. The largest amount of material requirements in these regions are derived from the refurbishment of the existing stock. Moreover, in areas where structural material is needed for new construction, in Asia, Africa and South America, rain forests need to be protected. Therefore, we need to rethink the desire to find one solution and carelessly implement it everywhere. Instead, we need to consider locally available material and know-how for grounded material choices. This paper explores the supply of a range of bio-based materials and matches it against the material demand of global building stocks. It is based on various previous studies by the authors, of South Africa, China, Portugal, and more. The analysis divides between structural materials for new construction, such as wood and bamboo, and thermal insulation materials for the refurbishment of existing buildings, such as straw and hemp. The results emphasize the need for diversifying bio-based material solutions.