The fixed 2x error factor works for those who are experienced enough to be able to enumerate everything that goes into project and avoid most surprises and problems (and predict the amount of time used to solve "surprising" issues).
Then, obviously, the fact that there is this mystic 2x factor to begin with, is just ridiculous. But at least for me, it is there; it's psychology! Even if we are experienced, we are not always fully sensible.
In theory, if someone is able to estimate the time with such consistent 2x error factor, nothing prevents them from just making a correct estimate to begin with; just multiply by two. In theory. But psychology comes into play. We think we have already multiplied it by two, do we need to do it again?
Clients also want to hear optimistic schedules. Many even understand and accept that project timelines stretch. If you give them the honest timeline, they add 2-3x on the top of it, and say "no" to the project. Yet as a designer, you need to be honest and cannot safely assume such behavior. I have solved this by being more verbose about the timeline so that it's not a single number, but we reach at least some kind of understanding how the project actually works out.
It's all psychology.