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I've seen older literature that just uses "cycles," "kilocycles," and so forth.

It's never abbreviated, so I always assumed the use of a named unit came from the desire to be able to write shorthand like kHz.

I’ve absolutely seen it abbreviated. The wikipedia page even shows a photo of a “1000 kc” crystal resonator.

https://en.wikipedia.org/wiki/Cycle_per_second

Seems annoying if you’re a physicist or RF engineer. The Hertz makes sense.

We just used cycles per second (cps). Or multiples of it. Hertz was simply the name give to this unit, first in 1935, and later was included in the SI units in 1960.

Hertz are really only appropriate for describing cyclical events. But by convention the units are just 1/s, so have fun abusing it.

A period of infinity is cyclical /s

One interesting property of Hertz is that it's partially appropriate for describing sampling rates. I've found use in annotating separate units for "cycles/sec" and "samples/sec" so I avoid mixing them up (for example, the Nyquist rate can be expressed as 0.5 cyc/smp).