I served in USS JOHN F. KENNEDY (CV67) and completed my Officer of the Deck qualification, so I can respond. There’s two answers-

1. The OOD, while launching and recovering aircraft, maneuvers the ship to keep the apparent wind coming straight down the angle deck at the speed requested by the Air Officer (Air Boss) in Primary Flight Control (PriFli). This was typically ten degrees to port and around twenty-five knots.
2. If the true wind direction wasn’t favorable, the ship would, indeed, be going away from the Plan of Intended Movement (PIM). Then the ship would have to proceed at a high speed to get back on PIM. It wouldn’t be “hundreds of miles” behind, but ships don’t go all that fast. JFK could make 28 knots with four boilers in operation.
3. If PIM was based on a 15 knot transit speed and you wound up 25 miles from where you wanted to be, it could take several hours to get back on track. Of course, by then, it’s time for the next flight cycle and once again you find yourself going in the direction you don’t want.