Beyond a formal preference for background independence, what is stopping us from setting cosmological time as a de facto universal timeline, analogous to newtonian absolute time? General relativity doesn't entail it on its own, but neither does it forbid us if certain conditions hold (for a given model.)
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The cosmological time is the longest proper time possible since the big bang and the only hypersurface of constant t in which the universe is isotropic, but other than that it is not special, the equations of general relativity also hold in any other reference frame so you can do it, but you don't have to.
Also the comoving observers who experience t to be their τ are not at rest relative to each other, so that alone is already different than under Newton. Nevertheless, a fast neutrino created at the big bang will always have a lower proper time than a comoving observer when they fly past each other and compare their clocks.
Yukterez
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Lee Smolin argues for an alternate conception of relativity in which there exists a preferred cosmological time throughout the universe. See his book Time Reborn for an introduction to this idea.
niels nielsen
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