To render it useless for a while is easier.
https://en.wikipedia.org/wiki/USS_Enterprise_fire
All from a little drone-sized warhead.
(~20kg warhead)
This is Trump's America, brother, we don't learn from the past here!
Of course, this assumes the carrier is within range of the drone swarm, but that seems to be the assumption in this line of argument.
Eventually, I think they'll have more cost-effective defenses against small, cheap drones, but they don't have them yet.
Unfortunately warships have a lot of flammables and explosives aboard.