No, I'm not; you're just mistaken about which classical results I was referring to. I meant the results of classical EM that predicted that atoms could not exist--because the electrons would radiate until they fell into the nucleus. And what classical formula tells you how much the electrons will radiate because of their acceleration due to responding to the electric field of the nucleus? Larmor's formula.

In other words, Larmor's formula was not a "theory"--it was a particular result derived within a theory. The particular result happened to be correct, within a particular limited domain; but the underlying theory that was used to derive it could not explain why it was correct--because the same theory, and indeed the same particular result--the same formula--made other predictions that were obviously egregiously wrong (like predicting that atoms would collapse).

> nobody succeeded in obtaining the emission line frequencies of gases out of the classical EM theory

You're drastically understating the failure of classical EM here. It's not that classical EM couldn't predict the particular frequencies of emission lines. It's that classical EM couldn't predict the existence of emission lines at all. Classical EM predicted that atoms would emit a continuous spectrum of radiation--not radiation sharply peaked at particular frequencies.

> The classical formula is taught to this day both in macroscopic EM theory and quantum optics courses

Sure, because within its domain of validity, it works fine as an approximation. But that's all it is--an approximation. And we explain why the approximation works, and why it works only within a particular domain of validity, by reference to the more complete underlying theory--quantum electrodynamics.

> I do not know what you mean by "correct".

I mean "makes predictions that match the results of experiments".

I agree; but there's a big difference between:

- A theory that is incomplete because it doesn't cover absolutely everything, including where we haven't tested yet and won't be able to for the foreseeable future, but makes correct predictions everywhere we can actually test it; and

- A theory that is incomplete because it makes predictions about some things that are obviously at variance with observation, even though it makes correct predictions about others.

GR is an incomplete theory in the former sense; and theories that are incomplete in that sense can still be used to safely rule out competing theories that don't match their predictions in regimes where those predictions have been extensively confirmed.

However, classical electromagnetism is an incomplete theory in the latter sense; it made obviously wrong predictions, like the ultraviolet catastrophe and the instability of atoms. And even the correct predictions it made, like using the Larmor formula to predict radiative properties of atoms, were only obtained by using the theory inconsistently: by first assuming, contrary to the classical EM prediction, that atoms could be stable at all, and then working out what classical EM said about how these impossible objects (impossible according to classical EM) could radiate.

In a situation like that, you can't safely use the theory to rule out other theories, because the theory contradicts itself, and you can prove anything from contradictory assumptions. That's why classical EM physicists couldn't say "well, the Schrodinger theory can't be right, because I can't use it to derive the Larmor formula". You can't consistently use classical EM to derive the Larmor formula either; you have to sweep certain things under the rug and wave your hands that somehow or other it's ok.

In a situation like the latter, yes, you're right that anything that can give some handle on making predictions is going to be at least tried. But that's a very different situation from the former situation, where we have a correct theory that, within its domain of validity, doesn't have any of those issues. The only issue with GR is that it's not a quantum theory, which means, in the eyes of many physicists, that it's incomplete; but that incompleteness has no practical consequences whatsoever. It certainly is not a reason to entertain alternative theories of gravitational waves that get other predictions wrong that GR gets right.