A minute is an insignificant period for most daily tasks, so the convention "show me when the minute changes" is simple and pragmatic. If your task needs precise count of seconds, you get a clock that shows when the second changes, and now you are half a second late on average.
You can keep playing with increasingly smaller time units until you conclude, like Zeno's arrow paradox, that you're always infinitely late.
Pointless remark about myself, but I always set my phone's clock to second precision (I think this setting is hidden somewhere, or even needs a third-party app to unlock), and I am annoyed there's no way to do this on the lockscreen. How is it possible that nobody else (apparently) wants it, and it's not the Android default? Why would I want a clock that is, on average, a half minute off?
> Why would I want a clock that is, on average, a half minute off?
Because in 99.9% of the cases I don't care about the seconds, it takes away space in the top status bar, and the constant changing of seconds in the top-left corner of the screen is distracting. And for the remaining 0.1% of cases, there is the clock app that shows seconds.
What benefit do you gain in daily life by having the time down to the second? The argument "so it's not half a minute off on average" seems a bit self-referential.
> What benefit do you gain in daily life by having the time down to the second?
I commute by public transport and am sometimes cutting it fine, so knowing whether it is hh:mm:05 or hh:mm:55 does make a difference in how much I have to hurry up sometimes.
> and I am annoyed there's no way to do this on the lockscreen
With some OEMs there is (personally I know that current-ish Sony phones offer a corresponding option), but yeah, it is a bit annoying that that isn't universal… part of the reason I still carry a regular watch.
You can keep playing with increasingly smaller time units until you conclude, like Zeno's arrow paradox, that you're always infinitely late.