Sometimes we use the variable s to represent semiperimeter rather than using P/2, and we know that s is just half of the perimeter. Why can't we do the same with pi and tau? Tau is the more fundamental constant, so it would be the one used in cases where either is simpler or where tau is simpler, but in formulas where pi is simpler, we can still use pi and define it as tau/2. This way, the formulas that pi does simplify are both simple and intuitive; people will see the pi there and know that there is a factor of 1/2. Pi could be used as a shorthand for 1/2*tau just as semiperimeter is used as a shorthand for 1/2*perimeter.