I think there is very strong reason to think of GR as just a mathematical model. I know it has been successful for over a century, and a lot of people (maybe most) think that it is not just a theory - it is reality.
But no, it is just a mathematical model. I think the initial assumption that "spaced is curved" is retained because it yields excellent results - it has predictive power. But, it is inherently absurd, and besides good results, it also yields absurdities:
- The black hole information paradox for example. An actual paradox.
- Dark energy. Violates conservation of energy.
- Inflation. A kluge. A massive kluge invoked to explain how the cosmic background radiation can be so uniform.
- Incompatibility with the Standard Model of Particle Physics. Speaks for itself.
At the root of all these absurdities is the assumption that space is curved. I conclude that there might be a different mechanism at work.