One naive question one might ask is, what is time? If time is a real tangible thing, and not just a reference variable stemming from the human imagination, I would like to see someone convert a bottle of time, into another tangible thing. Time is in so many equations that define how other tangible things work and interact. I can turn matter into energy, or momentum into heat, etc. How about converting time into energy, as a demonstration that time is a real thing? For example, we can solve for time in the kinetic energy equation. This should tell us how to interact the tangible things like mass and energy, to convert time, using an experiment. If we can't do this, than either the theory is weak or time is more of a reference variable.
Time, as a reference variable, is needed because so many equations make use of it. If you got rid of time, even based on sound logic, all these same equations will need major modifications, That is a lot of work, and would make the experts, who use time, seem obsolete. It is much easier to suppress the few, than do the work or do the experiments as I propose. The C ground state creates the same practical problem, or a need to re-tool all the equations. But in both cases, it is far more powerful for predictions, since phenomena will not be reference dependent.
There is no time in general relativity, Barbour's approach is totally consistent, just in case you fail to understand. There just isn't a global time in relativity.
For example, if you look at the universe from the POV of a black hole reference, it sees a different energy balance than we see on earth. Many of the earth centric theories of the universe, could not be supported from the black hole reference. All energy coming into the black hole reference, from the universe, will be blue shifted, by GR, relative to what we see on earth. This will make the universe seem hotter. The black hole reference scientists would need different theories to explain this extra heat.
If we use the timeless state of C as the ground state, both earth and the black hole theory will agree. But again, this means work, while suppression is easier than the idea of starting over again.