I caught a carp (low double) yesterday that swallowed the hook right down. Size 14 barbless, but it could have been a bigger hook on another day. I always have a small disgorger, mainly for little fish, and forceps for larger hooks/fish. The hook was too deep, so I cut the line reckoning the carp could probably throw the hook.
But someone there said you should always have a very long disgorger as you can then get the hook out even if it's gone right down into the stomach.
Hmm, I am not sure it would have worked, and it's the first time it's ever happened with a carp, so I'm inclined to ignore the advice. But I'd be interested in the view of others on A.N.