[2022] Just a question from an old guy.

CVs can fight CVs. It's commonly term'd a "CV Snipe". Carriers have fighters that patrol over the hull, so it limits attacks to one drop only (in almost all cases). This means it can take 4-7+ minutes for a CV to fly all the way across the map just to attack and sink an enemy CV. Because this amount of time investment is so long, it's not done very often. Still, it happens. Especially if Battleships can tag some damage into the CV Hull to speed up the process.

Subs can fight Subs, as well. They have a consumable which is specifically made for fighting other subs, but it takes around 4-5 minutes to activate after game start. The reasoning is so that subs have time to get into sneaky positions before they start fighting, and then the consumables are available for subs to fight each other after they've had a chance to sneak around for a while.