> Biologists certainly don't. What is a species? Is Linnean taxonomy useful or merely confusing and obsolete? What is a gene?

These are human definitions for classifications, and biologists agree on that. However, if you make a statement that "two groups of animals that can never reproduce successfully with each other are separate species" then nobody will argue that. Similarly, nobody argues about what the mechanism is for species reproduction success or failure. Everyone knows how chromosomes and DNA works. There's no debate.

Every chemist uses the same periodic table with the same elements. Etc...

> What would such an explanation look like

Equations that can be evaluated numerically that shows the behaviour of the EM field, in 4D spacetime, capable of demonstrating interactions with charged particles. That's all. That's not asking much.

> why do you think that there is such an explanation?

Because it's a thing that happens. There are atoms that have electrons that electromagnetically interact with light and change orbits.

Quantum Mechanics provides a highly simplified model of this in a very narrow use-case. That's not wrong, or mathematically invalid. But it's not the whole picture, and isn't a valid source from which to answer questions like "what is a photon".

That's not describing the nature of light in the real physical world, it describes the nature of an abstraction in a simplified model. The photon exists in the equations. That's why it's so hard to visualise and "pin down" with a simple description. It's a property of the model, not the world.

> We can build up a set of observations and build a formal model to summarize them whose terms we can map to the results of various observations.

The models in this case are tiny subsets of all physical behaviour and generally only cover certain categories of scalar observables. E.g.: "The detector went off or not". Hence the cartoon diagrams and focus on the observables covered by the model.

> But there is no requirement that the model be able to satisfy queries that depend on things that don't exist in the domain of the model.

I agree. But photons are a thing that exist in the model. What I'm saying is that the photons exist only in the model.

> Sure, because you're not asking a question about anything observable

See, you made the same mistake as everyone else! Atoms aren't the only things that exist! There are free particles in vacuum chambers, particle accelerators, outer space, etc... that aren't atoms. There's a device called a "free electron laser" that has a continuously adjustable output frequency!

> There's a charged thing wiggling somewhere, and the interaction between two charged things that wiggle is quantized.

Only if they're in potential wells. Even then it's not entirely clear if all interactions are quantised.

> I can calculate the transition probability

That output is a scalar. The electron is in an orbital though, right? With a defined angular momentum, position in space, and everything. Even if you abandon the concept of point particles, it has a bunch of properties. Now show me all of those properties changing as it absorbs the photon.

Classic QM can't, because it doesn't even try. It focuses on the narrow case of "near resonance" light and then handwaves over how the photons actually change their orbitals. Cartoon diagrams and statistics. That's fine if you're designing a laser or something, but that's not what is physically happening with a single electron around a single atom.