With CV AAA and puffy ack as lethal as it is, I say a CV shouldn't be allowed to park off a field, even if nobody is actively trying to shell anything. This thing would have been spotted and sunk 100 miles before it got off shore of a major airfield.
But having AI shore batteries fire and sink CVs if they get too close, you wouldn't have this anymore. Either 1) People move a CV in too close trying to be weak/lame and it is sunk, or 2) They are actively USING the CV and up sorties to bomb/kill the AI SBs before they sink the CV. In that case -- if they are serious -- there's no problem. In the case of CVs harrassing airfleids, the AI will protect them and stop the milk runners or griefers.