if you need to deal with this, you must present estimates as ranges or distributions. Management needs a value for both concrete, legit purposes like budgets and also for (still legitimate) psychological reasons like building comfort that they know what's going on and they are in control. As you mention, people will anchor on a number and that in a nutshell is how an estimate becomes a deadline. Planning and execution will refine the value right up to the point you ship with a very accurate estimate of "how long do you think this will take?".