We argue that the possibility to observe a stable biaxial nematic phas
e in a binary mixture of prolate and oblate hard particles is seriousl
y limited by the existence of entropy-driven demixing. This result fol
lows from a simple Onsager-type density functional theory. An importan
t feature is the coupling of the demixing mechanism to the orientation
al order of the system. The strength of this coupling is dependent on
the asphericity of the particles, and is directly related to the stabi
lity of the biaxial nematic phase.