First I would like to dispel the common misconception that the ship’s forward motion relative to the water requires the pilot to aim for a point forward of the intended point of landing. It does not. The approach is flown the same whether the ship is stationary or moving.
For any pilots out there, do you aim for a different landing point on the runway depending on the wind? Probably not, you shoot for the landing area and adjust the controls for the effects of wind to arrive in the same spot every time. If winds are calm you need less power to maintain glideslope, if winds are strong you will need more power for the same glideslope.
It is the same thing at the boat. We don’t care about our motion relative to the water, only the ship and the wind matters.
Now, I flew steam gauge Prowlers so I can’t speak to the HUD, but my Hornet friends would tell me that they initially put the velocity vector in the notch between the end of the landing area and the port side forward. So, this is a little forward of the intended touchdown point, but not nearly as exaggerated as the screen captures I've seen depict. The pilot should then fly other visual cues to touchdown. I would presume that as the computer stabilized and updated as they came down the groove that the pipper would settle right in the landing area.
However, without the benefit of a HUD there is zero pilot adjustment made for ship’s forward motion. And even with this tool the flight computer should adjust for the effect of wind and put the pipper in the landing area where the plane is headed, right?
Bottom line, we don’t care about or even notice the aircraft or ship motion relative to the water during final approach. Our perception, and the net effect of the ship’s forward progress, is on wind only. We are trained to fly glideslope, line-up, and aircraft angle of attack all the way to touchdown. Overthinking things only leads to confusion, and spotting the deck is highly discouraged.
There are a few caveats to that last paragraph concerning ship motion: We make note of natural vs ship generated wind. When there are whitecaps and little to no ship’s wake we anticipate natural winds right down the angle. If the sea is calm and there is a boiling wake behind the ship we know the ship is steaming hard to make wind, so there will be a slight right crosswind and some turbulence from the island.
Pitching decks have been talked to death so I won’t expound on that in this answer…
And finally, the ship may turn during your approach. They really try not to, but sometimes they do, and it can make chasing line-up a bit sporty!
To summarize and answer the main question, landing on an aircraft carrier isn’t inherently all that much more difficult than other aviation tasks that require a high degree of precision. I have been into a pretty tiny little runway, and been bounced around by wicked crosswinds in light civil aircraft and it put a very similar level of strain on my pilot skills.
A big part of it is mental. There are plenty of good pilots out there who can fly an ILS on the rails that would probably make it in Naval Aviation. It just takes a level of commitment, training, and discipline to succeed over a sustained period time.
P.S. I have 300+ traps and was a wing qualified LSO in case anyone is wondering about my credentials.