Really interesting topic. (I’m actually somewhere in between sales and dev - doing Req. Engineering, Concepts and planning).

Personally I consider it more important to constantly narrow down any uncertainties over time, than having an initial estimate that holds. The closer it gets to any deadline, the less uncertainty I want (need) to have because the less options remain to react to changes.

And frankly, this usually not only applies to estimates but also to things that these estimates rely upon. The longer the timeline, the more room for circumstances and requirements to change.