Because when you are measuring the power of any signal besides a perfect CW tone you have to specify the bandwidth it's measured in. If you were comparing two CW tones it would be dBc. Comparing a tone to noise must be dBc/Hz. Also, it's in dB because it's easier to add than multiply. If you want to know the thermal noise power in a 1 kHz bandwidth is simply -174 dBm/Hz + 30 dBHz = -144 dBm. That's a simple example but when you have to do a link budget with all sorts of parameters you'll see why it's easier to take logarithms and scribble the answer out on paper.
It´s not a natural law - that means you also could specify/measure it, for example, in a 3.5-Hz bandwidth. However, would this make sense ?
If you normalize to a 1-Hz bandwidth you have only to multiply with the actual bandwidth to get the effective noise level referenced to the carrier.
So if you need to get noise power, in a specific bandwidth, you should integrate it over frequency (calculate the spectrum area inside bandwidth).
However, spectral density vs frequency is not constant (except for white noise), so u need to know the power in a small bandwith, the smaller the better, 1Hz is appropriate. Thus u can know precisely the spectrum shape and can calculate power in a specific bandwidth.
Because spectrum is not flat, for oscillators the noise is given as dBc/Hz at x KHz offset from central frequency. An unit as dB/MHz is usefull only if the noise power is quite constant in a 1MHz bandwidth, egg thermal noise, but not for an oscillator.