Is the difference in quality of life so dramatic with a day wrapping on non-integer seconds when both proposals wrap at non-integer minutes and non-integer hours?
The real question is why stop at miliseconds - it seems inconsequential. Go all the way down and assume that as the hour/minute/second granularity all proved insufficient in the past, the same way milliseconds would become insufficient one day. Make the period parameterizable (i.e. not a constant), with only the current value at 24 hours 39 minutes 35 seconds 244 milliseconds.
The real question is why stop at miliseconds - it seems inconsequential. Go all the way down and assume that as the hour/minute/second granularity all proved insufficient in the past, the same way milliseconds would become insufficient one day. Make the period parameterizable (i.e. not a constant), with only the current value at 24 hours 39 minutes 35 seconds 244 milliseconds.