The presence of mass changes the metric of ('curves') space-time and objects follow timelike geodesics through space-time. Not sure what you want. We have a theory of gravity that works.
We have classical Newtonian physics, we have Relativity, and we have quantum mechanics. What we don't have, as far as I'm aware, is a single unifying theory that provides us with a working picture of the natural world. This, I gather, is certainly the case in relation to gravity.
Of course this only matters if you agree with Einstein's assertion that "The programmatic aim of all physics, is the complete description of any real situation as it supposedly exists". To be fair, the current orthodoxy seems to be with you, in that all that matters is not what is, but what works; "Shut up and calculate", as David Mermin said. This is most unsatisfying for philosophers though. And this is not a science forum.