It would be amazing, but it should be a decentralised app. Otherwise an central authority or corp would know how much you run and therefore how much you earn. Anyway, it would be a great idea since it would be real proof of work. Maybe professional runners will use it and they use to have many sponsors, here you have an idea on how to monetise it.
Discussion
If I was a billionaire this is the type of stuff I'd build.
Great! This is the point of money, achieving goals which are much more ambitious and unique than money itself. I think the time will come when bitcoiners will be able to change the world, I think we will see something like a new "Renaissance" but if it happens I think it will be in some decades from now. Time will tell...