Earlier quoted context omitted.
I don't find this rambling insightful at all. Here is what the BIPM actually says about the topic: The SI unit of frequency is hertz, the SI unit of angular velocity and angular frequency is radian per second, and the SI unit of activity is becquerel, implying counts per second. Although it is formally correct to write all three of these units as the reciprocal second, the use of the different names emphasizes the di…
Right, you can explain it but that doesn’t make it elegant. This is the equivalent of a function with a comment in it saying “Here be dragons!”. One very desirable property of a units system is that incompatible quantities have incompatible units. So if I try to add 1 Joule (== 1 kg⋅m^2⋅s^−2) to 1 meter, I’m obviously doing something wrong and I just can’t continue. But in SI I can take 1 Hertz (==1 s^-1) and add it…
More clear example: both Gy and Sv are J/kg (m^2 s^-2), but to add two values, one in each of those units, you need to multiply one of them by a coefficient (that coefficient depends on the kind of radiation and specific organ that absorbed this radiation). So somewhere in the math world lives a constant that is unitless 1, but x Sv/Gy, where x != 1 (again that x depends on circumstances).
Those situations just happen. It's how physics work.