This question is motivated by this question and this one, but I will try to write it in such a way that it is not duplicate. In short, I don't understand the motivation for a "quantum theory of gravity" that predicts a particle such as the graviton, because it stands in opposition to the entire framework of general relativity. Let me explain.
First, a personal comment: I am a mathematician with a general understanding of what GR is (I took an undergraduate course from Sean Carroll, which used Hartle's book because his own was not yet published). I know slightly less than the corresponding amount of QM, which I do understand at the level of "an observable is a Hermitian operator acting on a Hilbert space of which the wave function is an element"; I know nothing technical about QFT, though I believe that "a particle is a representation of the gauge group" is true. However, I do have a popular-science understanding of elementary particles (at the precise level of Asimov's Atom, which I read a lot in high school).
Now for the framing of the question. GR in a nutshell is that that spacetime is fundamentally a 4-manifold with a metric locally isomorphic to Minkowski space and that particles are timelike geodesics in this manifold. The force of gravity only appears as such when these geodesics (i.e. curves) are parametrized in a coordinate patch, where "geodesic" and "coordinatewise unaccelerated" are different concepts; the apparent acceleration seems to reflect a force (via Newton's second law) that we experience as gravity. This phenomenon is identical to the appearance of a centrifugal force in a rotating coordinate system where none exists in a stationary one (it is identical in that this is a particular instance of it).
I understand that the standard model is formulated in a flat spacetime, and its use for the hypothetical graviton is to mediate the force of gravity. I also understand that quantum gravity is a (shall we say) paradigm in which the standard model is made consistent with GR, and that the hallmark of a theory of quantum gravity is that it predicts a graviton. But this seems to be barking up the wrong tree: you cannot remove the geometry from GR without changing it entirely, but you cannot consider gravity a force (and thus, have a corresponding quantum particle) without removing the geometry.
It does seem from this question that I have oversimplified somewhat, however, in that some theories, which I had thought were not very mainstream, do treat gravity in an "emergent" manner rather than as an interaction.
My question: What I want to know is: rather than pursuing a "quantum theory of gravity", why not pursue a "gravitational quantum theory"? That is: since the formulation of standard quantum physics is not background independent in that it requires a flat spacetime, it cannot be compatible with GR in any complete way. At best it can be expanded to a local theory of quantum gravity. Why is it that (apparently) mainstream opinion treats GR as the outlier that must be correctly localized to fit the standard model, rather than as the necessary framework that supports a globalization of the standard model? One in which the graviton is not a particle in the global picture, but a fictitious object that appears from formulating this global theory in local coordinates?
PS. I have seen this question and this one, which are obviously in the same direction I describe. They discuss the related question of whether GR can be derived from other principles, which is definitely a more consistent take on the unification problem. I suppose this means that part of my question is: why must Einstein's spacetime be replaced? Why can't the pseudo-Riemannian geometry picture be the fundamental one?
Edit: I have now also seen this question, which is extremely similar, but the main answer doesn't satisfy me in that it confirms the existence of the problem I'm talking about but doesn't explain why it exists.
PPS. I'd appreciate answers at the same level as that of the question. I don't know jargon and I'm not familiar with any theoretical physics past third-year undergrad. If you want to use these things in your answer you'll have to unravel them a bit so that, at least, I know what explicit theoretical dependencies I need to follow you.