> You don't need to sink an aircraft carrier, just keep it at long range.
At which point you haven't neutralised it; it's just become a 'fleet in being'. You still have to account for it. You may be able to protect your home waters from it, but you can't project power when it's around.
A country like Egypt, Iran or China could keep carriers out of territorial waters or block key choke points in their region with diesel subs or mine. A moderate projection of force could block the straight of Malacca and damage operations.
Even if you didn't sink the carrier, you could wound it, which would be worse than a sinking in some ways. At best you can keep it a few hundred miles away, which will render its future complement of short-range F-35s safely neutered. Alternatively, you probably just need to sink a few container ships to get the desired outcome.