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Hertz, becquerel, et al. are algebraically defined as s^(-1) yet intended to be used for different kinds of quantities. The SI brochure also allows replacing radian by 1, which brings angular velocity into the fight. Further reading: https://doi.org/10.1088/0026-1394/52/1/40

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And that brings up the difference between frequency and angular frequency.

When you use hertz meaning ‘cycles per second’ it’s far more natural to associate it with an angular velocity of 2pi radians per second - which throws a bit of a spanner in the dimensionless works, and makes it feel like using 1/2pi as a radian makes more sense.

Score another point for tau I guess.

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