Apple has not made the necessary APIs available. Only those two apps have animated icons. They’re made by Apple and so they are able to use the private APIs needed to do it.
IIRC, the clock and calendar ones are a hack, with code in Springboard actually drawing the icons. Or at least that’s how it was at the start.
Maybe they’ve refactored it into a private API by now, though any such API would involve icon-drawing app extensions sort of like widgets, which seems a bit heavy if only a few system apps will have it as a gimmick.
Same deal on Android. OEM launcher apps override the app icons for the OEM's calendar and clock apps, and there is no way for a different app to achieve the same effect.