w/r relativistic effects and continental drift - not really. The speed is about 1cm/yr or v = 1e-18 c. Relativistic effect would go like 0.5 * (v/c)**2, so more like 5E-37 in relative rate of proper time. You can just barely capture a few minutes of that even with int128 resolution. As for financial incentive for int128, considering the super-rich will get exponentially more rich while inflation devalues the possession of the rest, the super-rich will eventually have demand for int128 to be able to count their wealth down to the last ct. It's a lot for money, though. A lot more than the net value of all real things on the planet. But the net value of assets on people's bank accounts already exceeds that number by some factor 50-100, and this factor will grow exponentially as more financial "products" are being created. When I was a student (~1990) we had to create new bookkeeping software using int64 ("comp") because the investment company could not deal with billions of dollars worth of Italian Lira down to centimos otherwise. Accounting needs will get us int128, sooner than you think, don't worry.
Yes, it would be good to create routines than can handle time in units provided, maybe as a string. Or you could just create a time object that handles this internally, e.g., algebraic operations, similar to numpy, at the accuracy available. You can access its value by providing the desired divisor, and you may inquires the available precision. If you want to handle this properly, it may get you back to interval arithmetics.
Regarding concerns about the effect of gravity on your computer, there will be a press release in a few h that may be of interest to some
-Alexander