Sinking or even just seriously damaging a U.S. aircraft carrier — approx. 5K people in crew + airwing, billions of dollars in ship and aircraft — might trigger a Pearl-Harbor or 9/11 fury among the American public. No U.S. president could get away with even a "proportionate" response, let alone doing nothing.
Think of the Tonkin Gulf incident in 1965, which led to the U.S.'s widened involvement in Vietnam on the basis of grossly-distorted reports about alleged attacks — which never happened — on U.S. destroyers (which are comparatively small ships). [0] If Iran were to actually sink a U.S. aircraft carrier, then Trump-Hegseth-Miller might well nuke Tehran in response.
We sure as hell don't need anything like the assassination of Archduke Franz Ferdinand in Sarajevo in 1914 by a terrorist. It triggered a cascade of some of the stupidest and costliest government decisions in history. Belgrade, Vienna, St. Petersburg, Berlin, Paris, London, they all effed it up almost beyond belief. WWI cost millions of lives and untold billions in resources that could have been put to far better use. Iran sinking a U.S. carrier could be a similar trigger.