Earlier quoted context omitted.
If we have military hegemony, then why can't we open the strait of Hormuz?
Because it would require a boots on the ground invasion to occupy the entire portion of Iran overlooking the Strait. The strait is physically open but no insurance company will cover massive oil carriers because they are so easy to hit with small weaponry from the ridges of Iran.
And even if they had to pay a claim, it would cost the population less than the higher gas prices, since increasing supply lowers the market price for all supply, not just the incremental units.