"Just" taking Karg Island, 300 km of coastline, and 4 other tiny islands leaves the US occupying forces as sitting ducks under constant bombardment and drone attacks from the Iranian mainland.

US service members would be constantly getting killed, causing inevitable escalation and deeper and deeper incursions. It's a quagmire.

This stuff is the exact same reason Israel constantly feels the need to peel more territory off their neighbours after each war. "We're getting bombed near the borders, so we need to push our borders out to keep the border regions safe", which of course just creates a new, even bigger border region.