Time is inherent to the universe. So is space. Which is why the universe is also referred to as space-time.
This is patently and absurdly false. Firstly, it should be obvious that for Newton and for physicists after Newton, both time and space were "inherent" to the universe (things are rather more subtle, but as this remains the case after Einstein we can gloss over that for now), and it was and remains possible to speak about spacetimes that are not relativistic or that satisfy Galilean relativity in which the time dimension is completely separated from those of space.
Second, when Minkowski introduced spacetime after Einstein introduced special relativity, Einstein was initially rather vehemently opposed to what he saw as an unnecessary introduction of geometry and the corresponding spacetime it introduced into what were better seen as algebraic derivations from his two postulates (he did change his mind on this). The point being that the relevance of spacetime was not seen by the founder of relativity nor was it initially a pleasing result (still less a
reason to refer to the intermingling of space and time in relativistic physics as "spacetime").
Third, the importance of spacetime in physics is not at all due to the fact that "Time is inherent to the universe" and that "[ so ] is space." Ohanian puts this more concisely than I probably can:
"As a physicist, I think that philosophers of science have overstated their case for a real 4D world. By mistake or by exaggeration, they have endowed the theory of relativity and the inertial coordinates commonly used in this theory with deep layers of meaning that are not justified by the physics. On the basis of physics, it can be asserted that space-time is a 4D manifold with a 4D geometry, but whether the real world – that is, the totality of all the material things that inhabit spacetime – is 4D or 3D, cannot be decided by physics. Both 4D and 3D descriptions of material systems are possible in physics, and physicists use both of these modes of description interchangeably." (p. 81)
Ohanian, H. C. (2007). The Real World and Space-Time. In V. Petkov (Ed.).
Relativity and the Dimensionality and the World (
Fundamental Theories of Physics Vol. 153) (pp. 81-100). Springer.
In fact, demanding that, because spatial and time coordinates in relativistic physics become "intermingled" (e.g., transformations from one reference frame to another cannot be done in terms of some absolute, Newtonian time) creates a number of problems in "spacetime" physics as well as fundamental physics more generally. In relativistic physics, one consequence (not really a problem) is that we need time in order to have kinematics and dynamics (and more importantly the equations of motion of any particular theory cast in whatever formulation and in terms of whatever entities it is). So immediately in special relativity after introducing a new geometry with either of the two signatures one has to introduce a dynamical parameter like "proper time" which is outside of spacetime. This becomes vastly more complicated in GR, where one relies on parallel transport, covariance, and so forth to make use of the tangent and cotangent bundles for what used to be a simple linear transformation.
For me, the bigger issue is (unsurprisingly) the way in which one cannot simply demand that
Time is inherent to the universe. So is space.
and think the physics will follow. This is because (as I have emphasized repeatedly elsewhere) that in quantum mechanics as in classical (non-relativistic) physics time is a parameter while space is treated fundamentally differently via algebras of observables as an operator. It turns out to be basically impossible to treat time as an operator, so in "do" quantum theory in spacetime one must demote "position" from an operator. Then the problem becomes what the resulting relativistic quantum mechanics is a theory about. In order to avoid causal violations even when performing local measurements, or even just to make sense out of the formalism, one has to give up on notions rather central to quantum mechanics (such as particle number conservation, or position measurements, or more basically the idea that there exists quantum systems that can be modeled experimentally by state preparation and some observable of interest represented by the appropriate operator).
In cosmology and the QFT(s) of particle physics (and QFT more generally) one reinterprets the operators as
being the particles or physical entities, so that they can act locally on some spacetime which is itself reinterpreted in terms of a vacuum state that the newly minted operators-as-particles act on. What, in NRQM, is typically called raising and lowering (along with the operators of the same name) becomes creation and annihilation. These now act on "fields" which by virtue of being fields need not follow the same conservation laws but must necessarily be local (just as their classical analogues) and by acting on the "fields" (which is where we manage to finagle things in order to get space and time on some sort of equal footing) we can make the operators act locally and reconceptualize as well as reinterpret the entire scheme in terms of "particles" acting local spacetime "states".
We still require time to exist outside of this spacetime approach in a myriad of ways (just recall, for example, the need for time-ordering exponentials in canonical quantization). The path integral approach differs, naturally, in how "dynamical" time is treated in relativistic quantum theory, but an "outside" time is still necessary and, moreover, the entire process is still lacking a rigorous mathematical definition for most of its uses anyway and relies more on heuristics that we are fine with but which are disturbing or nonsensical to mathematicians.
Finally, it is only the assumptions of certain symmetries that most be obeyed by any theories that require the use of spacetimes of any type in physics in the first place. While I can't really imagine how one could do physics without these, it is important to keep in mind that it is not experiment but the demand that one should not have to e.g. pick out a preferred basis or that one should be able to set initial conditions and so forth that lead to the need for space and time to be on the same footing. Then, as per the quote above, one should again keep in mind that just because some geometry, topology, space, spacetime, etc., is used in physics does not mean it should be taken to be reality. I rarely encounter anybody arguing that we must live in an infinite-dimensional complex-valued vector space equipped with an inner product that is complete in the norm just because the whole of quantum theory requires such spaces.