User WillO wrote the following comment:
why isn't Minkowski space a counterexample to the expectation you
attribute to Einstein?
I will write a temporary answer here, as it is too large to fit into a comment. WillO, if you submit your question as a new question I will move this answer to that new page.
About Einstein's expectation:
Einstein had a hunch that the existence of inertia (in the universe) is due to all of the presence of inertial mass in the Universe, in the sense that perhaps all of the inertial mass in the Universe combined is what gives rise to the existence of inertia in the Universe. If that is the case then a Universe without any inertial mass in it would not have inertia. It is my understanding that the solution called 'De Sitter space' is at odds with that hunch.
About the difference between Minkowski spacetime and GR spacetime:
John Wheeler coined the following summary: 'Matter is telling space how to curve, space is telling matter how to move' Of course that was not intended as an accurate description; the purpose was to focus on a specific feature. In terms of GR spacetime is a dynamic participant in the physics taking place. Spacetime is affected by (lumps of) inertial mass, taking on curvature.
Where GR spacetime is a dynamic entity, Minkowski spacetime is a static entity. Minkowski spacetime does affect the physical processes occurring in it, as illustrated by the Twin scenario, but Minkowski spacetime itself is not subject to any form of change.
As we know, universal Minkowski spacetime is incompatible with GR.
We have the succession of three theories of space and time
Newtonian space and time
At both stages of that succession sequence the old theory is a limiting case of the theory that superceded it.
Special relativity superseded Newtonian space and time. Limiting case: in the realm of non-relativistic velocities the mathematical expressions simplify to newtonian dynamics
General Relativity superseded Special Relativity. Limiting case: in the realm of negligable curvature GR spacetime is observationally indistinguishable from Minkowski spacetime.
In terms of GR Minkowski spacetime is an obsolete concept, part of the previous theory of space and time.