If little Iran can prevent the US from being able to establish security in a little straight, it (ideally) shatters that image and causes some soul searching for what US taxpayers are buying with the military.
And just like the Vietnamese, Iran doesn’t have to win against the US. They only have to not lose. They control the straight, and at $1 per barrel toll, they’ll be making $1 Billion a week. Trump owned himself. This is going to suck.
Regardless of the analogies, the reality is that even with all the resources the US spent on its military, after a whole month, it cannot guarantee safe passage through a body of water adjacent to a small time adversary. Which, as an American, is embarrassing in terms of ROI on tax dollars spent.
To put it in perspective - in Vietnam, opposition forces lost over a million troops and continued to fight viciously. The US lost around 50,000 and gave up and left.
Democratic countries simply lack the stomach for this kind of thing (which is a good thing, really).
Obviously, there were other things going on in Vietnam (and Afghanistan and the larger War on Terror) to keep them fighting but it's much easier to muster up the manpower when a war seems existential because it's happening in your neighborhood.