You start learning circling skills earlier because they require more timing and strength to perform and therefore longer to learn. So it's not so much that you learn a half-pirouette later, but that you learn circling elements earlier or that's my understanding of it.
Some gymnasts also find it harder to hold their feet up so to not hit the ground out of a turning skill than a circling skill.
Why does it come so late in USAG (yes level 8 is correct)? Because USAG has deemed the skill a C and only level 8s and above can do C level skills except circling elements to handstand which are also Cs. This is what USAG has deemed. Level 6s and 7s can't do Cs, except for circling elements (free-hip, toe-circle, and stalder), which are an exception.
It is totally possible to do a circling element directly out of a half pirouette, and even easier to do a circling element to handstand and then pirouette.