FACT 2 - a carrier is probably one of the best ways to project influence and statemetns about military intent in coastal areas.
American aircraft carrier fans have been saying junk such as that for sixty years or more.
"Put some of our big carriers offshore! That'll show that tinpot dictator we mean business!"
But it never works. The tinpot dictators are unimpressed, even the smallest, dinky-est little dumps such as Panama or Grenada.
To get the bad boss, tinpot or otherwise, out of power, the USA always ends up having to people on the ground in country in sufficient strength.
... I guess it's ancient history now, but the USAF and USN carrier aviation had been bombing Iraq for years and years before 2003. The bombing didn't make the late Saddam H. retire.