You aren't appreciating just how good modern defensive armaments really are, and how hard it is to destroy an aircraft carrier. And you are overestimating what a really cheap drone can do.
Lets look at the drone. If you want several thousand of them (lets say 4000) "cheaply" then you are spending, what?, $1.1 billion on an equivalent of a $275,000 plane - like a Cessna 172. Cruise speed 140 mph - this is only 4 times faster the ships; its never exceed speed is 188 MPH, total load (including fuel) 750 lb. There are cheaper cars that drive faster. And that $1.1 billion is not exactly chickenfeed.
In the slow crawl out to engage the fleet (3 hours to hit it 420 miles out) the fleet can relocate 100 miles. Makes a dense coordinated attack impossible even if you can track the fleet in real time.
The Phalanx CIWS (Close In Weapon System) that every U.S. combat ship carries is designed to shoot down missiles up to 10 times faster with a much smaller profile with high reliability. The Phalanx success against "soft ball" targets such as you propose is essentially perfect. A carrier strike group deploys at least 8 of these on four ships that can provide mutual support and together can engage 40 targets a minute indefinitely or 200 targets all at once. Of course if this threat was known to exist, they can double up on supporting combat ships if needed for additional Phalanxes, perhaps to double this engagement capacity. And then there is that air wing that can surge enough fire power during this period to engage roughly 1000 targets.
So the air wing gets to thin out any close clumps of targets far out from the fleet so that the CIWS crews can watch their system clean up the rest. Since there is enough time for up 25 CIWS engagements for each target (more if the ships are staggered) there is no chance that even one would reach a ship.
And then there is the ability for the group to lay down a smoke curtain - an ancient tactic. It still works against cameras, but not against the radar-guided defensive weapons.
An accident on the USS Forrestal during the Vietnam War led to nine bombs exploding on-board, the ship returned to service nine months later. The current Nimitz Class aircraft carrier is two-thirds larger and even harder to sink.
This proposal is not unusual to hear from people unfamiliar with the effort put into defending ships.