Good point about CV and CVL escorts not engaging the enemy. I normally put CLs in with CVs, for the added range and better firepower if needed, which is fine for spotting and air-striking subs because the planes are the main spotters, but I prefer large DD fleets to actually sink the subs. If you put both fleets on patrol in the same province, they'll very likely just go in different directions, so you might need to manually send them back and forth on Aggressive stance through the subs' usual patrol areas, It's not until about the 1941 or '42 tech levels that CAGs develop enough firepower to actually kill subs before they break contact, unless you stack 3 or more CVs in a fleet.
My fastest CVLs normally go into battle fleets with BBs to provide air cover for the BBs against any possible hostile carriers, the slower ones get used as sub spotters, and the true CVs get their own fleets to support the battle fleets without drawing off the BBs' escorts to protect the CVs. You do NOT want to mix BBs and CVs in the same fleet because the escorts will abandon the BBs to protect the more valuable carriers, while the BBs eat 100% of the incoming fire at poor evasion odds and sink. The less valuable CVLs don't cause a problem (unless the CVLs are slower than the BBs and hold back the entire fleet).
Note that if you play Germany, you'll need at least one level of Carrier Engine tech for your first CVL, otherwise it won't even keep up with the old WWI Baltic Fleet Battlecruisers. Bismarck and Tirpitz will require CVLs with a few more levels of engine tech to match their faster pace (playing GER, I always research the 1936 level of engine tech before building my first BB, which will still complete well before hostilities start if I build one or two BCs to boost my Capital Ship Practical value). The same engine tech principle applies for any country planning to build carriers: either put your first CVL in its own anti-submarine fleet, or hold off construction until you've got enough levels of Engine tech to keep pace with the ships it's intended to work with. All other carrier techs are secondary to that essential Engine tech. Building an initial CVL is usually a good idea for any country planning to build CVs, even if you have no use for an escort carrier, just to speed up research and production of future full CVs. The cost savings on the first CV can just about half-way pay for the CVL, and shave months off the completion date.
Be aware that ALL ships in a port will fire at any planes you sent to attack the port or ships in it, so don't port-strike someplace with 40 ships in the province if you value your CAGs or NAVs.