This was all theory before the war. Now Iran knows they can blockade that Strait and makes these demands so they have much more leverage.
Tehran has more potential leverage inasmuch as they've credibly demonstrated they can block the Strait. Whether they have more actual leverage than before is uncertain–trade flows are routing around them. And their own shores remain blockaded. (Just because the U.S. has less leverage than it did before doesn't mean Iran necessarily has more.)
"Shut down" is not particularly accurate. America and Europe can route around. The only ones fucked are the Gulf carriers.