Power density graph does not work for signals that have infinitely narrow peaks.
If you had a signal with a continuous static frequency and plotted the power density of it in infinite resolution, the graph would have a spike of infinite height.
Practical power density graphs, like the one shown, have a limited horizontal resolution. The frequency domain is sampled at some interval, for example 1 Hz. Even if the signal had a peak narrower than this, it would get averaged out in the graph. When the graph has limited horizontal resolution, it does not provide useful information of bandwidths narrower than this.
It is easy to define a mathematical signal that has non-zero power at 0 Hz bandwidth: sin(x). We can even get quite close to pure sine wave in real-world signal generators. But any spectrum measurement for finite length of time will have a limit on the frequency resolution, causing the peak to get averaged out to more than 0 Hz. Mathematically the power spectrum of this signal would be Dirac delta: δ(f).