Got a Second?

The Clock app on iOS has barely changed since iPhone OS 1.0. And that's fine, because world clocks, alarms, stopwatches, and timers are pretty widely understood and don’t need constant redesigning.
But there’s something odd, something that’s bothered me forever. There’s nowhere in the app to view the current time with seconds.
The only place on iOS to view the progress of a minute is in the Clock app icon, which shows the current time including a second hand. But kind of awkwardly, when searching from the App Library, its app icon is only right twice a day; it’s permanently 10:09:30. The Calendar app icon, by comparison, displays the current day and date when searching from the App Library, so there’s not a system incapability of dynamic app icons in those search results.