The hertz is not dimensionally identified as 1/T, despite the fact that this has been voted in 1995 by the clueless delegates to the CGPM.
The hertz is a name for cycle per second and the physical quantity that is measured in hertz is plane angle per time a.k.a. phase angle per time, not reciprocal time.
According to your proposal, phase angle must not be dimensionless, right?