In the real world of actual experience, I'd like to question whether or not you can easily separate the "fear of the state of being dead" from "the fear of the process of dying".
This year I got the flu twice, and it was really bad in January, and slightly not as painful when I got it at the start of November. Everyone knows both from experience and modern medicine that most people that are in generally good health recover from the flu. But imagine experiencing some sickness and not knowing if you were going to die from it. Even now with modern medicine, there are times when it is unclear if a sick or injured person is going to recover or eventually die, and so that uncertainty could cause anxiety.
It would seem that if you "feel okay with" the concept of death, then the process of dying should theoretically not cause as much anxiety.
Here is a movie that might go with this discussion: