I have posted this before and it may be controversial (it may even be wrong) but there is a mode of thought backed by many that aircraft carriers have not had a decisive effect since 1982. Every other operation since could have been launched without carrier launched aircraft.
I think you will find that the use of TacAir in Afghanistan post 9/11 could not have happened without carrier launched a/c ( no host nation available for land based offensive air). Also the Al Faw assault was largely launched from Ark Royal and OCEAN (I think).