The tricky thing is that the US doesn’t want to blow up Kharg island, because that would spike oil prices. More discussion is in the Phillips P. O’Brien link above. O’Brien is Professor of Strategic Studies at University of St Andrews.
ETA: Occupation has complications. If Iran can’t get its oil out, why should they let the Saudis get the oil out? Oil infrastructure is difficult to defend. As are marines sitting on the island given the sorts of missiles Iran has. And Iran can choke Hormuz shipments further. It’s a risky gambit, one which requires careful gaming and thinking.