Intuitive explanation of coherence
It feels like any wave at a particular frequency will have a constant phase difference relative to all waves with the same frequency, but from the explanation in the paragraph above that would mean that coherence should be 1 across every frequency for every signal.


I think you're falling into the frequency-domain trap.  The frequency domain is nice, but it was invented to use when thinking in the time domain is harder.  If thinking in the time domain is easier -- don't try to wedge things into the frequency domain, unless you have to for some other part of the problem.

So if you have two signals that are predominantly sinusoidal, and if they're both frequency modulated, then you'll have something like $$s_n(t) = \cos\left( \int \omega_n(t) dt\right)$$ where $\omega_n(t)$ is a random process.  If $\omega_1(t)$ exactly equals $\omega_2(t)$ then your signals will be coherent -- even if $\omega_1$ and $\omega_2$ are time-varying.  If $\omega_1(t)$ and $\omega_2(t)$ have equal long-term averages, but small differences at any given time, then your signals will show some coherence (depending on how you assign numbers to "small differences" and "some coherence").  If $\omega_1(t)$ and $\omega_2(t)$ are unrelated, then your signals will have no coherence.

But note: this is really flipping hard to analyze in the frequency domain and not too bad to think about in the time domain.  So thank M. Fourier for all his hard work, do this analysis in the time domain, and then use the frequency domain the next time you really need it.