Base e for life.
This technique will definitely be applied to exoplanets as the angular resolution and spectroscopic sensitivity are improved. In fact, improvements to both if these numbers are being relentlessly pursued by a veritable army of scientists around the world.
Spectral broadening only needs one pixel, and enough spectral sensitivity that the broadening isn’t entirely in the margin of error. We are pushing For ever more accurate spectral sensitivity as we try to use Doppler measurement to hunt for exoplanets.
Meanwhile the ongoing efforts to obtain greater angular resolution, has basically been one of the core pursuits of the astronomical community for centuries. We are building massive telescopes and advanced compensation systems in the form of adaptive optics to get the very best out of these telescopes.
So yeah I think we’re going to have rotation rate measures before we see much more than a pale blue dot.
edit: I think it will lead to the same or more problems because everyone would have to change all time-related constants. Easier to add a second to the day constant (because the day constant is a subset of the seconds constant, but the seconds constant affects many more aspects than just the day constant).
[1]: https://en.wikipedia.org/wiki/Isotopes_of_caesium#Caesium-13...