Hertz seems to be considered a fundamental and atomic unit that we modulate or analyze. 112Hz, 113Hz, etc. Wouldn't we have more to work with if we considered sub-Hertz granularity, e.g. 112.5Hz, 112.59Hz? Why isn't this done (on a wide scale)?
Why don't we see carrier frequencies in communications systems like this for example?
Tagging 'fourier' because I don't know how else to tag this.
Why isn't this done (on a wide scale)?
It is widely done. I have no idea why you think it isn't.
See for example a typical chart for the frequencies of musical notes: https://pages.mtu.edu/~suits/notefreqs.html or https://en.wikipedia.org/wiki/Piano_key_frequencies
These all use sub 1Hz resolution. Otherwise you'd be playing terribly out of tune, especially at the low frequencies.
