My comment referred to your statement about the size of datasets with
2**53 entries. The need to specify time (or other variables) to great
precision is separate from the need to store a great deal of data in a
given dataset.
If what you say is true (and I don't doubt it) about our ability to
exactly recover integers from stored doubles, then using a double for
time does solve *our* problem. Those who really need the extra precision
would still need another solution.