>the wave analogy stop being relevant at this point?

It doesn't stop being relevant, you just have an incorrect picture of what is happening. You likely are basing this image on your intuition of waves of water.

Actually, a useful image is more like sound waves. A sound wave consists of oscillating pressure in some medium, such as air or even water. When you hear sound, do you just hear the "high" pressure peaks? Or the low pressure valleys? Or, do you hear the full range of changes over some period of time?

It's the latter.

In fact, if you were only hearing the "peaks" or the top half or the bottom half of a sound wave, you would hear something that is distorted. This is actually how sound distortion in music works, such as for guitar amps or synthesizers. When we speak, or a piano hammers a tuned string, the sound created is relatively smooth, like a sine wave (speaking has more complicated wave patterns but the patterns consist of a combination of relatively smooth waves). A distorted sound appears more like a square wave or something with more corners on it, when plotted visually. So instead of your ear sensing the smooth undulations of pressure changes, it experiences sustained pressure (such as the top of a square wave) followed by (or preceding) a much more abrupt and instantaneous change (the vertical part of a square wave). This is more jarring and unexpected, which is why it sounds "unnatural."

Vision and light share some of these characteristics of experience, in that when your eyes see, they are typically experiencing a smooth range of changes in the Electromagnetic spectrum over time as the photon passes the receptors in your eye. It's not simply the peaks or valleys of this wave, it is the frequency and the total energy ( simply: how many photons in the frequency range) that your eyes sense. You can't really experience an instant of a photon. You need the changes of the wave over time for your body and brain to sense and interpret these signals.