Why is landing on a carrier not handled by a computer?
Computers can, in fact, control the approach of a Super Hornet all the way to touchdown.  However, there are limits to the sea state. Gross deviations in glide path resulting from a pitching deck would make a coupled approach impractical.

However, the most compelling reason to hand fly all our approaches is that we fly a $60 million jet. Murphy's Law tells us that the most junior guy, with the least experience behind the boat, is going to get an engine fire, at night, in rough seas.  If our fictional JO wasn't proficient hand flying the ball behind the boat this could result in catastrophic consequences including both the loss of aircrew and aircraft. As often as possible, we prepare for the 1 percentile, not the 99th percentile, so when we do get that engine fire at night we get the upgrade OK, and not the cut pass/ ejection.

Plus, its just plain eerie letting the jet fly itself to the boat, and the current system isn't reliable enough that most guys would feel comfortable letting it fly itself on a regular basis.

Edit:  Heck, new guys aren't even allowed to perform auto approaches (auto throttle) to the boat for the same reason.