My completely ridiculous supposition:

Any ships with an ACI are unlikely to have a shipgirl. The human tendency to personify the inanimate creates shipgirls by long-term exposure to Spengler flux from the crew. Larger ships have larger crews, so they are more likely to reach the critical point that generates a shipgirl.

The relative age of a shipgirl is based on when they reached that critical point, and when they reached end of mortal existence. Thus, a destroyer will tend to produce a younger shipgirl if it has one at all, and carriers and battleships generally produce older shipgirls.

A ship with an ACI already has a personality, and the crew will tend to focus on that, rather than personifying the ship.

Peter Eng
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Insert humorous comment here.