If it's an extremely hostile environment one can imagine a sub carrier and a conventional carrier operating in tandem.
The sub carrier goes as close to the target as possible and surfaces just long enough to launch strike fighters. The conventional carrier stays a safer distance away in order to pick up the fighters after the attack.
If you and your enemy both have (for example) fighters with a range of 3000km, you could launch 500km from the target, hit, and run for pickup to a carrier 2000km from the target. The enemy interceptors couldn't follow you to the pickup carrier because they need to preserve enough fuel to return home.
The thing is with a sub carrier, it is a HVU, or a High Value Unit. If the presence of one is suspected, you can expect that a lot of enemy assets will be deployed to attack it. Therefore, there is a need to escort a HVU. A carrier never goes to sea without an escort, even on trials. The problem here is that submarines rarely like to operate with friendly ships in close proximity, which is required to escort a HVU. It ties submarine commander's hands, and introduces a more easily detectable target that could give away the presence of the submarine. You are going to have to think about the bigger picture: how are you going to escort such a ship (there is no way in hell that such a valuable target be not escorted)? How are you going to conduct flight ops under rough weather due to the low freeboard and shallow draft? A war ain't going to be paused because there is rough weather.
A carrier is meant to be a beacon of permanent power projection; it is meant to bust its way into an area, and sustain a presence there. A submarine aircraft carrier cannot do either; it cannot break its way into an area and sustain a presence. Such a design, may I state this clearly, IS NOT PRACTICAL, even with the advances of technology seen today.
If I know a enemy submarine is in an area, and it is a important one or it is close to my assets, I will flood the area with ASW assets to hunt it down. Submarines are extremely vulnerable ships, often one hit and they are often done for. Surface carriers have the advantage of first of all, being able to continuously fight back 24/7 with aircraft, sustain high tempo flight ops in any weather, and take significantly more punishment than any submerged platform.