If you seize Qeshm, and the surrounding islets, as per the 1988 plans, you would go a long way to securing access to the Straits of Hormuz, including controlling the access of vessals connected to Iran. Both islands would be tough nuts to take and secure, but seizing Kharg has zero military reason. The entire value in seizing Kharg would depend on the invader assigning the same value to it as Iran. Ultimately, Iran has other means to shift oil out by other means. Iran might not care. But in seizing Qeshm, it doesn't matter what Iran thinks of that, you have greatly reduced its ability to interfere in shipping.
