"The world is made of kisses and not stones" (Rovelli)
Waves are in some sense the prototypes of transmission of influence without stuff also being transmitted, so could or should play a leading role in reflecting this insight (generally, and for good reason, any elaboration of the idea of a field comes after the idea of a wave). So it is rather important that the theoretical idea of a wave gets well-established in a way that the power and applicability of the idea across different contexts can be realised. So if we’re teaching about waves, then we’d like children be able to represent and reason about disparate phenomena using ideas that are distinctively wave-like. Such a demand requires that we have first in the front-of-mind a clear idea of a wave transposed from its natural rather algebraic realm into a form that is not diluted to the point of being a classificatory label for certain kinds of phenomena. To be teaching the idea of a wave is to capture the essence inherent in y = Asin(kx -ωt).
This is noticeably absent from the pre-16 physics criteria in the UK 2018(for example, it is one of 7 headings in the IGSE, yet the detail does not express the idea of delayed mimicry, or the idea of superposition). The idea of a wave is also not salient in the professional discussions amongst teachers of physics, for example on TalkPhysics or PTNC. Nor is it a feature of pupil textbooks, or teacher guidance associated with purchased materials. So there remains a largely unexplored question of how an immaterial approach to waves can support these interaction models rather than tending to reify the waves, or to elide without comment some of the essential features of the wave.
To further illuminate the issue, here is a piece of advice from a coach of teachers of physics, appearing high on search engine rankings: "Get the students to wave to you and they all can. So they understand the concepts of waves. Have a discussion of what makes a wave, a wave." [There is no indication of how to achieve the discrimination, or what such a distinction would look like on the page, or perhaps the site].
It may be somewhat harsh but the majority of highly rated teacher-advice sites, as located by search engine, are a series of declarative statements, often without any discernible cognitive glue, which might serve either to provide coherence, or to illuminate a pattern of thinking which the learner could apprehend.
This gap seems to me to be of a historical habit of mind – perhaps even a 'teacher ritual', as elsewhere there remain many other buttressing resources available, which do not follow this 'inessentials' approach. For example swell and surf forecasts focus on amplitudes, frequencies and expected arrival times, depending on the paths followed from the source.