The limiting factor in a cat launch is usually the hold-back pin on the plane, which connects the steam catapult shuttle to the plane.
(I only spent a brief time as a plane captain, so the details are forgotten.)
A catapult that is set "too hot", typically due to a miscommunication of the plane's gross weight, will rip the pin right off the plane, resulting in a "cold shot", which is rather unpleasant for the crew of the plane. A cold shot either leaves the plane sitting on the deck wondering what the hell happened, or they launch without enough energy.
As a plane guard helo I picked up a couple crews that went swimming when their multi-million dollar didn't get enough kick from the cat shot. Very angry about it too.
The steam cats can overpower any bird on the ship.
I never heard of a plane not being able to launch due to a lack of wind over the deck.
And someone mentioned that wind over the deck is needed for landing- to an extent this is true.
A plane on final at sea l will be faster than a plane on final at a land based field would be, typically 10-30 kts for a faster.
The difference, as you all know, is the arresting wires.
Carrier planes try to maintain more energy, or airspeed, when the wheels hit, to allow a bolter in case of a missed wire or fouled deck.
From watching flight ops while circling the carrier (for hours and hours), I don't believe the wind over the deck is as much of an issue as it used to be in the days of prop planes.
More of a question for a pilot though.