Carrier CAS does automatically fight in naval battles (unless you've sent it away to do ground support over land). The usual reason people displace CAS with more NAV is because they don't care about ground support, and find the NAV more effective at eliminating enemy fleets. If your doctrine (that is, player plans and intentions, not the game research doctrine) calls for carriers to be only anti-naval forces, you won't want the naval CAS.
If you want to give your invasions the edge of air support, you'll want some CAS, which aren't entirely useless in the anti-naval purpose, but also good for ground support, unlike NAV. Carriers can get your CAS close to the province being fought over, whereas with land-based air you don't always have a good nearby airfield, and you'll have to invade more places, closer together, to stay within your air cover. Carriers give your CAS more reach for a deeper threat. But of course, if your marines have sufficient superiority over the enemy, they perhaps can win even without any air support.
AFAIK, CAS without orders will not automatically join any nearby land combat. (The same goes for the other carrier planes; FTR will not automatically intercept bombers, or run air superiority in your sea zone, but only join naval combats, and NAV will not patrol or attack ships other than those that your carrier gets into battle with. Zone mission assignments are separate from naval engagements that planes join when their carrier is engaged and they have no mission assignment.)
I imagine that if carrier CAS flew off and joined a ground combat, leaving their carrier to get ambushed by an enemy fleet, and were blowing up tanks instead of enemy carriers or battleships, the forum would be inundated with complaints about carrier planes automatically going on missions, rather than complaints about them not automatically going on missions. The current system lets you assign them to one job or the other, so you have that much control -- but you do have to choose.
(The choice reminds me of the commonly-told story about Midway where Nagumo keeps changing his re-arming his planes to switch them between attacking Midway itself, or to attack nearby naval forces.)