Antiship missiles carry larger warheads, often double the size, and deliver that warhead deep inside a warship where it is much more vulnerable. A shahed blowing up on a carrier deck will be upsetting but won't do much. With particularly egregious negligence of standard US Navy damage control methodology, you might cause a lot of damage by fire, like what happened to the Ford. Not that I'm suggesting it was hit by a Shahed.

There's a plethora of various low cost systems being developed for some defence, but the assumption I always see on HN and elsewhere is that for some reason cheap offensive drones will just never have a countermeasure...which isn't how any of this works (exhibit A: massed infantry assaults can sometimes work against emplaced machine guns, but in general the machine gun was the end of that tactic).

There is absolutely no reason that the current disruption drones are causing should lead to some sustained power imbalance: if you don't have the big laser today that's one thing, but if tomorrow you're scoring 100% intercept rates against the same threat then how cheap it is doesn't matter anymore. And there's no particular reason to think that won't be the case (if a cheap drone can be on the offensive, you'd have to present a very good case why the interceptor cannot be built in similar quantities at which point you're back to high end systems deciding the day).