They claim air dominance - that means they control Iranian airspace and can fly around it at will. They have destroyed Iran's own air defences.
That doesn't mean the US can establish their own air defenses to protect Kharg island against a sustained attack. Those air defences don't currently exist so they'd have to set them up and Iran has shown itself perfectly capable of sending sustained drone and missile attacks. Carpet 'bomb' is probably the wrong term - it's carpet missile. Believe me, they send 500 drones and missiles at Kharg island (which isn't big) we end up with a very high US body count.
Iran is perfectly prepared to destroy its own assets to protect the regime. Would they definitely do it? No one knows but it's a strong enough possibility that the US military would be very reluctant to take the risk.
It also doesn't get the US anything. This is the issue with their position - they are fighting a war against a theoretical threat 1000s of miles from home against an opponent who is facing an existential threat. Iran is prepared to lose much more than US can. It's a similar position for Israel - the Israeli state sees Iran and Hezbollah as an existential threat. That's why one of the biggest worries most of the people on the ground in the region have is whether Israel is going to be willing to accept any peace that the US might want and, if they won't, what that means.