Traditional "manned" aircraft carriers may well be approaching an era of obsolescence. I agree that they are vulnerable, even the American ones. USA holds the advantage for now, but that advantage is tenuous and remains under threat from asymmetric means. The corollary of all this is that the status quo is very costly for USA, hence the Americans remain eager for a quick resolution. That said, what is very costly for USA is simultaneously crippling for Iran's economy.
Regardless of the logistics issues, USA may yet tolerate a long game of siege better than Iran can.