I am councilling exercising caution before broadcasting downgraded estimations of personal competence - in the hope of avoiding failures caused by the planning fallacy. This could very easily be one of the cases where evolution is smarter than you are.

If the finding that "when people made their predictions anonymously, they do not show the optimistic bias" is correct then, this isn't really much of a "fallacy" in the first place. It would then be more of a signalling strategy - broadly similar to putting in low dollar initial estimates in the hope of getting hired.

It might also be true that telling the truth about how long it will take me to do something will cause a planner who is using my inputs to estimate the overall project, and is accustomed to compensating for the planning fallacy in others, to miscalculate estimated time.

Of course, if they do that, there's a sense in which it's their fault rather than mine, which can matter when what we care about is assigning blame.

My usual way of splitting the difference is to give low, high, and most likely estimates. Pretty much uniformly, I'm then asked for a single number, and I ask which one they want and give it to them.