Absent the long-range (legacy P-3...future P-8 guys). you're all relegating it to the "Charlie's inside the wire!" construct. Too little...and too late. It's a "layered defense", yes? Who's doing the "outer layer"?
Speaking of helos, possibly. I get your point and if you're talking strictly CVN based helos, you're right. But there's other assets out there, as has been mentioned by several (like ghost, above). Also, just because the carrier is in the AOR doesn't mean all the helos are with it. There are tails out sniffing around with with an ASW bird looking, and they're not necessarily near the carrier. Finally, there's the P-x that's out there if it's the "right" AOR.
ASW can be broken down into 3 basic areas (this is just me talking, not any TTP stuff): planning/water space management (I just put myself to sleep typing that), using all the assets available in real time, effectively, and the actual button pushing to do the search/localization/tracking. When I hear about crews atrophying or "not as good" (which all may be true), I think of the button-pushing part. Maybe that's the wrong way to think of it, but I've always been on the operator side and not the planning/Alpha Sierra side.