And then confuse them later on. Remember how in early math classes they called those funky negative-under-a-square-root values from the quadratic formula imaginary numbers? A good lot of students get confused as hell for a while when they find out that not only are those values not "imaginary", but they pop up everywhere and have very tangible uses.

Once formulas make use of pi (and not 2*pi) later on, it's going to have to be defined as (tau/2), which is just going to end up confusing students.