Short answer: because tachyons don't exist (i.e. haven't been found)
Slightly longer answer: To be relative to spacetime would (most likely) mean having a means of transmitting information faster than the speed of light, but information cannot travel faster than the speed of light. * "The world line (or worldline) of an object is the path of that object in 4-dimensional spacetime, tracing the history of its location in space at each instant in time." [0] Something that would exist relative to spacetime (as in, would not be confined by the laws that dictate spacetime) would have to be outside of a light cone [1]; "In flat spacetime, the future light cone of an event is the boundary of its causal future and its past light cone is the boundary of its causal past."
* I don't know very much about quantum entanglement, so if anyone would like to comment as to whether entanglement might appear to violate transmission of information faster than c, that'd be neat, but i have a suspicion that it doesn't because either because of (A) a reason depending on the fact that qubits aren't like bits or (B) that the separation of two entangled subsystems would constitute the actual transmission of information but would still necessarily be no faster than c.
This isn't true. Given a manifold that satisfies the vacuum Einstein equations and given a world line in that manifold, it can be shown that the world line is undergoing acceleration using only local calculations/measurements. The worldline of a particle on the edge of a gyroscope will have a non-vanishing acceleration and this can be computed using local calculations/measurements.
You can describe the manifold using a coordinate system corotating with the gyroscope, the worldlines will still have a non-zero acceleration. There is absolutely no need for any matter field satisfying hyperbolic PDE's with faster than light characteristics.
Slightly longer answer: To be relative to spacetime would (most likely) mean having a means of transmitting information faster than the speed of light, but information cannot travel faster than the speed of light. * "The world line (or worldline) of an object is the path of that object in 4-dimensional spacetime, tracing the history of its location in space at each instant in time." [0] Something that would exist relative to spacetime (as in, would not be confined by the laws that dictate spacetime) would have to be outside of a light cone [1]; "In flat spacetime, the future light cone of an event is the boundary of its causal future and its past light cone is the boundary of its causal past."
https://en.wikipedia.org/wiki/World_line
https://en.wikipedia.org/wiki/Light_cone
* I don't know very much about quantum entanglement, so if anyone would like to comment as to whether entanglement might appear to violate transmission of information faster than c, that'd be neat, but i have a suspicion that it doesn't because either because of (A) a reason depending on the fact that qubits aren't like bits or (B) that the separation of two entangled subsystems would constitute the actual transmission of information but would still necessarily be no faster than c.