Modern science achieved objectivity by removing subjectivity from theory.

Yes, because the whole point of the material sciences is to describe reality as it exists independently of the subject.

Observers were treated as coordinate systems

Coordinate systems are more fundamental than observers. In Minkowski space, you can define a reference frame where an observer isn’t even present, in fact, you can even define a reference frame where no object is present at all.

Observers perceive different things in different physical contexts not because they are observers, but because they occupy different contexts. The physical context under which an observation takes place is more fundamental than the observer themselves.

and physical reality was assumed to exist independently of them.

Obviously the observer exists in physical reality. The point is not that materialists are pretending the observer doesn’t exist in physical reality, but that the conscious observer is not a fundamental feature of objective reality, and the things which they observe can be explained from pre-existing features in reality that would evolve in their own way even if the observer was not there to observe them.

But quantum mechanics introduced a strange situation: measurement determines physical outcomes, yet the observing subject itself is never defined within the theory.

Modern physicists tend to be highly pragmatic, prioritizing simplicity in their mathematics so it can be effectively used for calculations, engineering, and problem-solving, rather than worrying about philosophical questions.

If your goal is to strip away as many mathematical complexities as possible from predictive models due to pragmatic reasons, it’s easy to end up removing objective reality itself from the mathematics, creating a theory that only describes what appears on measurement devices and nothing beyond that.

The current formalism of quantum mechanics reflects this extreme pragmatism. Some academics, encountering this formalism, then slide into quantum mysticism, claiming that objective reality doesn’t exist until it’s observed, because the formalism doesn’t explicitly include it. But this is circular reasoning: the choice of formalism used to derive our ontology from requires justification. You cannot conclude that reality doesn’t exist simply because the formalism omits it; you must first justify why that particular formalism is the foundation for ontological claims.

In fact, it is entirely possible to construct quantum mechanical formalisms that do include objective reality. For instance, the physicist David Bohm developed a model of non-relativistic quantum predictions using point particles moving deterministically in 3D space, with well-defined positions at all times, independent of observation. The physicist Hrvoje Nikolić showed that this can indeed be extended to the relativistic domain as well.

This approach is less popular because it is mathematically more cumbersome. Most physicists favor the simpler, more pragmatic formalism that makes calculations easier. But the argument “objective reality is absent from the simplified formalism, therefore it doesn’t exist” is invalid. Any ontological conclusion requires an independent justification for why the simplified formalism should dictate our understanding of reality.

The observer is necessary

Under some formulations of the theory.