Some aren't, but this isn't a correct generalization.
...but this method has the risk of not doing a complete job...
Actually, the head comes off much more easily than you might imagine. One of the reasons skilled executioners were so highly valued is that the wrong drop would end up ripping the head off hanged convicts, which is unpleasant for onlookers. Once a table was devised, with drop heights based on weight, it was much less common, but with the vehicle, it's rather a moot point of "complete job"...it's more likely something else would go wrong. Or, as you said, kill innocents.
Surprising to many people is how "personal" methods are to suicidal people. They aren't interchangeable, and what is abhorrent to one person might be the preferred method of another.
Bump