The boom operator "flies" the boom down towards the receptacle when the pilot gets the plane in position. The boom moves and also extends out, so the boomer gets everything lined up and then extends the boom the last few inches until it plugs in. He has a console sort of like a complicated video game, that he uses to control everything and fly the boom around.
That's a lot easier than drogue/probe because with boom refuelling, both the plane and the boom are actively controlled and held stable. With drogue/probe, the probe is the only thing that is controlled. The drogue (basket) is just floating out there in the windstream, and any little airflow disturbance makes it bounce all over the place. Plus as the receiver gets close to the basket, the airflow around the plane pushes the basket out away from the plane just a bit.
There are other hazards with drogue/probe refuelling too. If the hose takeup reel is set wrong or malfunctions, too much slack can develop and very violent waves can form in the hose. When those waves get to the end, it can rip the probe right off of the receiver, or whack the plane causing severe damage. A bad or unlucky approach to the basket can also result in the basket getting briefly whipped away from the receiver and then snapping right back, punching a hole in the plane or doing other damage. Sucking it into the engine isn't really a problem unless something breaks off, and then yea the parts may end up down the intake.
The problem is that boom refuelling is complex and heavy, and the payoff just isn't there to adapt it to carrier plane use. I don't know if that's because they haven't tried hard enough, if it's a cultural resistance to change, or if it really isn't technically feasable, but you just won't see boom refuellers on carriers.
