Of course Schrodinger's model didn't reproduce the results of classical EM with regard to the atom. It wasn't supposed to, because those results of classical EM were wrong. In other words, there wasn't a correct "old theory" that covered the regime the Schrodinger model covered (the atom)--there was only a wrong "old theory".

As far as using Schrodinger's model plus classical EM theory to get results like emission line intensities, there also there was no correct "old theory"; there was only a wrong "old theory" (classical EM by itself, which did not predict emission lines at all, let alone their intensities--it predicted a continuous emission spectrum). Also, this hybrid classical-quantum model was known to be incomplete at the time; it was only used because nobody had yet figured out how to quantize the EM field.

> It is the new benefit that the theory brings, not reproduction of every single result of the previous theories

Once again, this is not the situation under discussion in this thread (gravitational waves). In the case you describe, the results of the previous theories were wrong in the regime the new model covered, so there was nothing to reproduce; there was no correct "old theory" for the new theory to compete with.

In the case of gravitational waves, we have a correct "old theory"--General Relativity--so any new theory that did not match that correct old theory would be a nonstarter. I am not aware of any case where a new theory was accepted as interesting when there was a correct old theory covering the same regime and the new theory did not reproduce its results.