Not so much escort as consort. Saying the carrier has escorts suggests that the other warships in a task group just defend the carrier, and that the carrier is passive. Submarines and frigates (in RN terminology) work in conjunction with the ASW helicopters. Continuously operating ASW helicopters around the clock requires a big deck with multiple aircraft.
Likewise a carrier's fighters are frequently controlled by an AAW destroyer.
All of this provides a defence over a large area, and the carrier may be used to protect things like amphibious forces or seaborne logistics - which was the main role of US and UK carriers during the Cold War, and is coming back to the fore in a new era of great power competition.
There must be a better term than 'escort'.