Yes. Bodies of matter in different spatial directions would need more evidence, but that’s not my premise. All I’m saying is that bodies of space can have their own time.
They can, yes, but whether or not we should take that as the default assumption is another matter entirely, and I believe DontTalk already provided a simple enough counterexample to that up there. The core premise of your argument seems to hinge on the idea that a temporal dimension is just a measure of spatial movement, and thus that spatially disjoint areas should have their own time-axes, but that's not necessarily true, as I'll further explain in the response below.
Since we use general relativity, the destruction of that space would destroy time, or the destruction of time would destroy that said space. Unless it’s proven otherwise.
What exactly do you mean by "the destruction of that space"? Due to how higher-dimensional spaces work, the universe of three dimensions we are familiar with is just a single slice out of the infinitely-many that comprise the spacetime continuum, and so arbitrarily removing some from the overall structure would hardly have any effect, much like how removing a single point out of the 1-dimensional real number line would result in... the same number line, but one where the choosen point was removed.
Granted, "destroying space" can also mean directly removing the axes themselves, instead of just objects that are extended in them, which is another can of worms entirely, but even in such a scenario, destroying space doesn't necessarily mean destroying time, either. Since, like DontTalk said in the previous thread, a fundamental property of a dimension is that it exists independently from other axes of the space which it forms.
To write up an in-depth explanation of why that's the case, I'll have to talk a bit about the concept of a
linear combination, which in the most intuitive terms possible is essentially a sum of two or more vectors, whose result is another vector of the same space.
For example, imagine three unit vectors (That is, the most basic vectors of a space, whose length is exactly 1),
a,
b and
c, and then multiply them by any triple of real numbers (in this case, that could be represented by a2, b4 and c6); a linear combination involving these three vectors would be a2 + b4 + c6, and since an unit vector's length is 1, the operation in this case is a trivial one and is the exact same thing as 2 + 4 + 6, with the only caveat being that these three numbers are being interpreted as each corresponding to the length of an individual vector.
For any set of vectors, we can also talk about its
span, which is just the set of all possible linear combinations that can be done with each of them, and in the case of the unit vectors of a space, their span is just the entirety of said space. For instance, the vectors (1,0,0), (0,1,0) and (0,0,1) have all of three-dimensional space as their span, since you can multiply them by any real number and then sum up the results to reach any point within the latter, with the total number of such combinations being infinite.
Now, like I mentioned before, a single vector can be written out as the linear combination of other vectors, and DontTalk provided a good practical example of that in the previous thread: North and East are separate directions from one another, but Northeast is not, since it is just the combination of the former two and thus can't exist without them. If that is the case with any vector, then we say it's "linearly dependent" of others.
On the other hand, we say a vector is linearly
independent if it cannot be expressed as the linear combination of other vectors, meaning it exists completely outside of their span and represents a new dimension. A good practical example of that would be saying that South is linearly independent from North and East: No possible combination of the latter two will ever allow you to go South, and so it's a different axis entirely.
So, the time dimension, being linearly independent from the other directions of the spacetime continuum, behaves in the exact same way. You might say that it only exists as a measure of spatial movement, sure, but that's not the entire picture when we are conceiving of time as something that physically exists; in such a case, it's just another direction, but one that we experience differently from the other three, and thus it can exist without them. So, if you erased the latter, you didn't create a dimensionless void, just reduced the universe to a 1-dimensional existence, which is a perfectly coherent notion. Quantum Field Theory uses models that have 0 spatial dimensions + 1 temporal, even,
as a quick search on Google can tell you.