> why is only change in space considered in the history of the universe

Gauge fixing.

There is no particular reason to slice up spacetime into spacelike hypersurfaces where each point in the hypersurface has the same time coordinate, other than convenience. Likewise, there is no particular reason to chose one set of time coordinates over another, other than convenience.

You can certainly work in 4 dimensional "block universe" when considering the radar distances between points on the worldlines that the centres-of-momentum of galaxies (or clusters) travel, and choose arbitrary coordinates. You're then using tensors for everything, and considering spacetime 4-volumes.

Slicing or threading into 3+1 resp 1+3 makes the calculations easier, but can introduce fictitious forces and other features that depend on one's choices when doing that sort of gauge fixing.

The standard cosmological frame of reference is a 3+1 slicing wherein the time coordinate is recoverable by an idealized observer locally measuring the spectrum of the CMB photons arriving at a point on the observer's worldline; such an observer will see matter in the bulk as homogeneous and isotropic, and will be far from any of the matter, and will see the CMB spectrum as equal to the emission spectrum of an ideal blackbody with a particular temperature. Add in adiabatic expansion, and the universe gives a quasi-universal time coordinate, which clamps many of the pseudo-forces 3+1 slicing can produce.

Since we are near lots of matter (the Earth, the solar system, our galaxy and the local cluster), we see big anisotropies and thus noise, including a gravitational and peculiar-motion redshift anisotropy in the CMB. As we get a better handle on our local environment, we can better strip out these factors that distinguish us real physical observers from an idealized non-physical "Eulerian" observer of a FLRW universe.

But since an alien astronomer in a far away galaxy could reasonably take the same approach, we could exchange messages like: "at our CMB temperature x K we observed a supernova in your galaxy", which the other side could relate to their measurement of the CMB temperature at time of supernova and at the time of receipt of message, and recover the equilvalent of a radar distance.

This also plays neatly with the Robertson-Walker (RW) spacetime that is fundamental to the cosmological frame: RW spacetimes readily admit a slicing which makes them higher-dimensional equivalents of a set of infinitesmially thin plates stacked one on top of the other, where the metric includes a function which determines the radius of each plate as one goes from the bottommost plate to the topmost. It also makes it easy to set down comoving coordinates such that matter stays at rest at the same spatial coordinates in every spacelike hypersurface: we expand the metric instead of actually moving the galaxies, which is good because there is no distortion of the shape of galaxy clusters implying a real (i.e., gauge-independent) acceleration in any particular direction, and because it makes it easy to take an Eulerian fluid mechanics approach to galaxy clusters in the large.

Additionally, this sort of slicing plays nicely with things like Hamiltonian mechanics and the time-dependent Schrödinger equation, which we are likely to care about when thinking about the microscopic details of events like a supernova inferrable from coarse-grained observables (like the emissions spectrum associated with supernova nucleosynthesis).

However, if something motivated you to do so, you could choose some other expanding-universe metric that is suitable for treating distant galaxies as at a lower gravitational potential, for instance. This would mean fixing a different gauge, and introducing some fictitious (gauge-dependent) forces to deal with some observables of high-redshift objects, and those would tend to complicate hypothetical communications with alien astronomers in distant galaxies. The "real" physics would -- just like the "real" physics in the cosmological frame -- be described correctly using generally covariant tensors. But you could do many calculations using simpler fields, and at least in principle that might highlight features that are obscured in the standard cosmological slicing.