And the whole point of Shrödinger's thought experiment was to ask how you get from the Shrödinger equation for an atom to a live or dead cat.
It didn't make any statement about the quantumness of the cat but rather asked how the quantumness of the atom gets transformed to certainty about the cat.

The Copenhagen interpretation is basically a trick stating that at some point the equations become too complex for us to handle them so we handwave them away by saying they "collapse" without actually giving a mathematical description of what that collapse really is and how the collapsed state is derived from the wave function.

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‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

I think that Schroedinger and Einstein both objected to the Copenhagen interpretation that wavefunction "collapse" was a kind of external piece of quantum mechanics, rather than something that can be internalized in quantum mechanics. The Copenhagen approach was to say that something fundamentally strange happened to quantum mechanics when you try to describe it in terms of classical apparatus, as we must always eventually do. Schroedinger and Einstein felt that this pointed to a problem in need of solving, Bohr and Heisenberg felt that anything which has no solution is not a problem worthy of consideration.
Note, however, that this "trick" is a pretty good description of what physics always does, in every case of practical interest. The goal of science is always simplification, and simplification always begins with pretense of some kind. The same holds for every published paper in physics or astronomy, so I agree with Bohr that the whole business is a tempest in a teacup.

I agree that simplification is what it's all about, but it's not good science it it doesn't then try to find a quantitative description of the simplified process and that to my mind is where the Copenhagen interpretation fails

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‘To those who regard “crime fiction” as some sacred icon which must follow a rigid formula, I will always be the man who writes 18-syllable haiku.’Trying to make sense of computers, The Error Log.

You are right that one can track more closely how wave function collapse occurs, say by looking at how random noise from the macroscopic instrument creeps into the calculation and causes decoherence. But my point is that criticizing the Copenhagen interpretion on the grounds that it does not track that process is like criticizing the ideal gas law because it doesn't tell us where every particle goes. All physical theories decide what they are going to care about, and what they will sweep under the rug, and the idea that any physical theory can be "complete" is just not recognizing what physics does. Some theories are more fundamental than others, but that's all one can ever say. The idea that any are "really fundamental" is a claim that I always find pretty puzzling, even though good physicists seem to claim things like that. They seem to have simply forgotten what they chose to pretend.