You might not know this but Hormuz sovereignty is a regime-legitimacy issue for the IRGC. They're not going to invite the country they call the Great Satan to comanage their most strategic asset so tankers can pass. That's the point. It doesn't matter what the Navy can or can't do. Iran will never agree to joint anything with the US on the strait.
You might not know that the US Navy has always had free and uninterrupted access to Hormuz. Nothing can stop a carrier squadron from passing through. This is not about the US military establishing presence there which it already has. This is about merchant ships.