Recently, I have been reading about the $\tau$ vs $\pi$ debate. One of the arguments for $\tau$ was that $1\tau$ radian is the whole circle, thus fractions of $\tau$ correspond to the fractions of the circle.
https://www.youtube.com/watch?v=jG7vhMMXagQ
But rather than thinking in terms of arc length, if we think in terms of the area of the circle, then $\pi$ does give us the whole circle, thus fractions of $\pi$ would correspond to the fractions of the circle.
What are some historic reasons for adopting the use of arc length (radian) rather than the area of the sector as the standard unit of angle?