[GrumpyYoungMan]

>If I hired a builder, and he told me that he refused to estimate the amount of money or time it would take to construct my property, you can be sure I'd move on. I have no idea why we'd consider it appropriate for an engineer to do this.

When every builder (i.e. engineering team) anyone ever hired everywhere blew through their estimate ~70% of the time, perhaps it's time to reconsider that stance. See the Standish Group's annual CHAOS Report for an example of software project success statistics, e.g.: https://www.infoq.com/articles/standish-chaos-2015

Estimates are just mutually agreed upon lies that engineering teams tell themselves.