Why does FM sound better than AM?

It's not merely an analogy, just the same EM waves scaled up in frequency by a few orders of magnitude.

Except that color isn’t the same thing as wavelength when it comes to humans perceiving light, because our eyes only deal with the total energy within each of three overlapping bands. An FM receiver knows the difference between a single carrier varying in frequency, and two carriers of different frequencies varying in proportion. Our eyes don’t, hence the banner above appearing orange, even though it’s actually made of different proportions of red and green.

Right, but let’s just consider the visual spectrum a single carrier/station

But that’s not how FM receivers generally work. They don’t just take a chunk of the spectrum and measure relative amplitudes within that window. Some very quick and dirty FM demodulators do something like that, but they have poor noise rejection, so the analogy fails.

Proper receivers use a phase-locked loop to “lock on” to a carrier, rejecting any weaker interference on nearby frequencies.

In the analogy, suppose you’re decoding a signal from a flashlight over the entire color spectrum, but sunlight shines through the leaves of the tree, adding a slight green noise component to what you see, while the flashlight is actually red. You’ll erroneously interpret the signal as slightly yellow.

We don’t have anything like the PLL in our eyes, so the analogy breaks down here. In the equivalent scenario with an actual FM signal, that slight “green” component would not affect the received signal (or it would affect it to a much lesser extent).