I find that it does get easier the more you do it, actually. Though that probably depends on your personality, or some critical mass of how many you must do before you reach the saturation point and get desensitized.
I had really annoying drainage problems when I first tried cervical dislocation on its own, without cutting the neck right after for drainage. I did the broomstick method and hung the bird upside down in the kill cone until it stopped kicking, then I cut the throat to drain it, and even though it had been just a couple of minutes, by that point it was too late - the blood had started coagulating inside the bird and would not easily flow out. I cut the whole head off and still only got a few drops. When I started processing, I found a giant glob of blood jelly in the neck under the skin (pulled by gravity and collected there before I cut the neck), and there was blood all over the organs, oozing out of the heart, and it made processing really messy and annoying. So now I make sure to cut the throat immediately after popping the neck, before I hang the bird, to make sure it drains properly.I know some say you won't get as good drainage that way, but I've never had an issue.