$1000 drones laden with explosives aiming for just above the waterline would seem to put holes in appropriately dangerous places.
You could launch a thousand of them for the cost of a single anti ship missile.
A reasonable thing to do in a modern war would be to launch 10,000 drones all at once at an aircraft carrier, even at a very low success rate that's a lot of little holes.
Just ask yourself how many you're going to need and what defense exists for them currently.
Shitty self-guided weapons can be made very easily these days and in tremendously large numbers. The defense industry focus is presently on very advanced things that it seems could trivially be overwhelmed by volume.
Double layer hulls? Compartmentalization? 1-8" thick steel plate?
When something floats, there are fewer restrictions on weight. CV-66 took a lot of direct explosions before going to the bottom.
The easiest way to think of modern carriers is ships inside ships, such that the entire thing stays buoyant even if most of the outside compartments are compromised.
Navies have been building steel ships for a minute... and are pretty good at it.
Welcome to the jeune ecole. The problem of $1000 drones is range and speed. A carrier is moving at 20kt, regularly. More if conducting flight operations. $1k drones are group 1 drones in DoD classification. There are limited in speed and range. If they teleported into range of the carrier, sure, they could reach it, and keep up with it. But if they don’t start near the carrier, how close do they need to start to do so?
To get holes at the water line, you’re going to have to take your drone down to the water line. Which means you’re going to have to deal with the waves and spray from being down there. Cheap drones are not notable for dealing well with hitting the water.
Beyond the thick steel plating, and compartmentalization, there’s also the fact that little holes just won’t let in much water. If you want to sink a ship, you need to let in more water than the pumps can take out.
If you start talking about $50k drones, then a bunch of these objections start changing. You can get much more range, much more speed, much larger warheads, and much greater capabilities in general. But your cost curve has changed a bunch, so you get 200 drones instead of 10k drones for a given amount of cash.
And at some point of additional requirements, you've come full circle back to the low-cost, rapid-production cruise missiles that most militaries (including the US) have been developing for the last 5 or so years.