In point of fact, any limb or beam will fail in compression before it fails in tension, unless there is a flaw in the tension surface, so, modulus of rupture is more a comparison of compression strength than tension.
Tension testing of wood is seldom done because the wood will fail in shear at the attachment points unless dimensions are greatly enlarged at the those points. And since wood fails first in either compression or shear, tension strength is much less important in engineering considerations.