Optimistically assume we as a species manage to survive to the point where distance, or relativistic speed differences, cause sufficiently frequent change in the observation of time passing that a single number, of any size, is no longer sufficient.

time_t is sufficient within bounds. It is expedient and quite correct in many computer science use cases. It can be extended with small additions for many other use cases.

However those bounds are a set of assumptions and simplifications that shouldn't be forgotten. I agree that the problem would be solved until the next paradigm shift in our understanding of time and the universe, and maybe forever if it turns out that the rules are cruel or we're too stupid to reach a more complex situation. I just wouldn't say once and for all, there's far too much uncertainty there.