Why are you asking “what happened each second” for the SI unit hertz, but not asking “what happened for a second” for the SI unit second?
The hertz is dimensionally identified as 1/T, and the second is dimensionally identified as T. These are both equally clear, at least dimensionally.
And if anything, the hertz is actually more specified in SI than the second, because the hertz is specifically reserved for describing periodic events, while the second can be used for many things beyond the amount of time between consecutive periodic events.
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.