I think "Losistic Ships" are a gross, but forgivable simplification of the whole issue. They made a certain amount of sense in AoA (kinda required for the plot as it worked out, and justifiable in an initial invasion force), but the idea that
a) the GTVA needs them to run the war effort when they control a 100% secure area within (conservatively) an hour from the front lines and
b) that one big ship is more practical than a multitude of smaller, more specialized ships to do every kind of logistical task, including refuelling, resupplying of everything from fuel and munitions to food and toilet paper, and large scale repairs is, well, pretty ridiculous. Even if the latter were true for whatever reason, as evidenced by WiH, they're way to valuable to the enemy to give them any chance at destroying/capturing them
However, as also evidenced by WiH, the missions where you capture this ship are fun, and that's far and away more important than any fridge logic issues regarding the Anemoi generally