Rachael Alexander won the Preakness today, not quite the impressive win that she had in the Kentucky Oaks, but she was running against better horses this time around, and she led wire to wire. As a reminder, a female horse is a 'filly' when she's 4 years old or younger and a 'mare' from then on, while a male 4 years old or younger is a 'colt' and then becomes a 'stallion' assuming his balls are still intact (and known as a gelding if they're not). When horses breed, 'sire' is the father and 'dam' is the mother.
The reason I was thinking about this is that it is rare for fillies to race, and even more rare for them to win big races going up against colts, because in general, colts are bigger, faster, and stronger. But from a horse breeding perspective, which is where a lot of the money comes from, I'd think that there should be huge demand for a fast filly: all mitochondria are maternally inherited, and mitochondria play a major role in energy production.
Certainly, there are benefits to having your breeding driven largely by males -- there's a much higher throughput if your impregnating rather than being impregnated. But having a proven dam passing on her mitochondria could give a substantial boost.