I think the time one is a good unpopular opinion. For example “day” is one of the most common time units there is. I really can’t see anyone advocating for a system that is unrelated to day/night cycle.
If night was to fall, sun was to rise and it wasn’t a new day yet? And the days ended at different times on different days? Absolutely no one would like that and we’d go back to using days almost instantly.
With that issue always in mind, you’re still bound to the earth’s rotation for every time-related issue (and a similar one around seasons also looms, for the earths orbit). And you’re back at square one.