In the Avalon Hill board game, the cruiser Atago is the flagship of a fleet of eight transports carrying 5,000 soldiers for the occupation of Midway. As such, it "represents" the transports and sinking the Atago is tantamount sinking the transports.
This move is worth some 20 points, four for the Atago itself, and 16 for each turn (on days 3 and 4) that the Americans hold Midway. Moreover, it deprives Japan of the chance to earn 15 points for capturing Midway, for a total swing of 35 points. For comparison, sinking a large carrier such as Japan's Kaga or America's Yorktown is worth 10 points.
Japan cannot defend the Atago against an all out attack. The only way to (indirectly) defend it is to (greatly) weaken the American airforce on the first day. As a practical matter, if the Americans lose their carriers but preserve 30 squadrons on Midway, it can sink the Atago.
As discussed in a previous question, the Americans maintain their advantage only by staying within range of Midway-based planes. If they go outside this range, they will be at a disadvantage. Might it therefore make sense for the Americans to wait for the Japanese to "come and get them" with the Atago? (This was NOT the strategy used in real life, where the Americans aggressively, and successfully went after the Japanese carriers early on the second day.