Live app icons on smartphones?

One thing on my iPhone that always makes me wonder is the Clock app icon. As far as I know, it is the only app icon that is actually "live" (constantly changing state to show the current time). There is also the Settings icon, with gears rotating, although only when updating. On Android, I don't know any app with this kind of behaviour, besides Calendar showing the current date.

I could not find any information regarding this feature in Apple Human-Interface Guidelines. I am not an iOS developer, so I am not sure whether this is even accessible to third-part developers or it is just reserved for system apps.

Basically I am curious about the UX implications of this feature. Is there any study regarding "live" app icons? Why don't Apple/Google or designers use it for more app icons?

(Also, do feature has a specific name? I used "live" based on Microsoft's live tiles.)