You can have both.
With Catapults, the speed of the boat is far less of an issue.
The F/A-18 takeoff speed is 140 knots, so how significant is 10 knots difference in takeoff speed with a Wasp or Type-076?
Look at the propulsion specifications for the Wasp class LHDs, which are roughly the same displacement as the Type-075/076
A single 26KW gas turbine gets the ship to 18 knots.
Two of these turbines (52KW) gets the ship to 22 knots.
But if you wanted to get to 30 knots, theoretically you would need 5 turbines (130KW of power), as per the 3rd power law.
So you get a lot more range and endurance with slower ship speeds.
When you combine this with low-speed drones, the aviation fuel requirements go way down as well.
That is why I see a dedicated escort carrier design (in the Wasp/Type-076 weight class) as being very complementary to a full scale carrier.