Definition of simpler - an argument for tau

[Eon]

It is stated that some formulas are simpler to write when using pi, but really does this matter? Is the end goal trying to minimize the amount of ink you need to print something?

To me a more valid argument is whether or not it is simpler to "see". To think about. To grasp. Tau radians per revolution makes sense. You can add integer multiples of tau to an angle to still mean the same angle. Nice and simple.

But ultimately why do we need to choose? Can't people use the one they are comfortable with? If I had to fight for something in mathematics it is this:

How can the definition of sin^n(x) suddenly change when n = -1? It is then said to mean arcsin instead of [sin(x)]^(-1) like with other values of n, in particular 2.

That, and, how can anyone still use 1-based indexing?