This is actually a technical question about what kind of mathematical practices and notation lead to a more energy-efficient society, and the expertise required to authoritatively answer this question for posterity's sake lies within this question's target audience. Thinking and computation in general (both human and non-human) are an energy and time-intensive process. Time and physical energy are scarce commodities in terms of the survival of an individual in a hyper-competitive society, and in terms of the survival of the entire society overall because the amount of energy a society can use for its survival is finite due to entropy and other factors. So this a technical question, but if anyone believes that this question can reach a more authoritative and influential group of respondents elsewhere please say so in the comments and I'll delete this and post it there instead. Also feel free to edit this post.
As many of you know, $\tau$ (tau) is defined as the length of the circumference of a circle of radius 1, and $π$ (pi) is defined as half of that circumference. Replacing radians with units of tau would, for example, lead to writing $\sin(90°) = \sin( π/2)$ as just $\sin(\tau/4)$ instead. Sin of a quarter of a circle. Easy. For three-quarters of a circle we just write $\sin(\tau*3/4)$ instead of $\sin( 2π*3/4) = \sin( π*3/2) = \sin(3*90°) = \sin(270°)$. So much precious time and effort was wasted in my high school math classes over this needless overcomplication. For a mathematicians, scientists, and engineers the difference in notation is trivial, but for first-time students its the difference between intellectual abuse and conceptual clarity.
EDIT: My original question also asked if we should replace radians with units of $\tau$ also. It turns out that that makes the derivatives of the trigonometric functions messy, because if $x$ is in units of $\tau$ instead of radians then the corresponding function for sine is $sin(x*\tau)$ and its derivative, in units of tau, is $\frac{d}{dx}sin(x\tau) = \tau*cos(x*\tau)$...I think. So radians are better and that part of my question has been definitively answered. Thank you.
Degrees are a useful convention that is not going away. Radians make calculus results very elegant. The derivative of $\sin x$ is $\cos x$ when $x$ is in radians. When $x$ is not in radians, it is something else. Radians and degrees are both important, and two systems of angle measurement are quite enough already.