That happens all the time with insurance. I'm surprised at the confident tone in "reality does not operate like this". Not just car/home insurance either...health insurance also. They do often negotiate to a reasonable place, but not always.

So when those times have occurred I've (we've more accurately) adopted what I refer to the "deer in the headlights" response to just about anything non-trivial. "Hoo boy, that could be doozy. I think someone on the team needs to take an hour or so and figure out what this is really going to take." Then you'll get asked to "ballpark it" because that's what managers do, and they get a number that makes them rise up in their chair, and yes, that is the number they remember. And then you do your hour of due diligence, and try your best not to actually give any other number than the ballpark at any time, and then you get it done "ahead of time" and look good.

Now, I've had good managers who totally didn't need this strategy, and I loved 'em to death. But for the other numbnuts who can't be bothered to learn their career skills, they get the whites of my eyes.

Also, just made meetings a lot more fun.

Due to small side projects like the painting of the Sistine Chapel ceiling it took around 40.

Failure to meet the deadline informed by the estimate meant that the scale of the project was massively reduced because: Pope Julius II had died prior to completion, there were changes requested by the customer (both Julius and his heirs), supply chain issues, contract renegotiations, labor disputes, shortages of qualified workers, and money running out due to the long duration of the project.

So, since 1505 at least?

The funny thing is that the pope isn't even interred there.

Conversely, if you're trying to launch a space probe and the planets are no longer in the right positions for the required gravity assist, your spacecraft will not get where it needs to go. Or if you're a little $100M/yr toolmaker, and Ford asks you for a die for the 2026 F150 production line, to be delivered by March, and the contract states you owe a $20,000 per MINUTE penalty if you're late...you don't wait until February to say something surprising happened and it's not going to be ready. You don't sign on that dotted line unless you know for certain that you can do it.

Ford or NASA won't bat an eye when you tell them that a quote is going to cost $XX,XXX. They won't be surprised when they give you an ECO and you say that it's going to take 3 weeks and $8,000 to deliver a part that everyone knows you can probably make by hand in 30 minutes, they know that you're hedging against those deadlines, and pricing in the acceptance phase and inspection phase and contingency plans and everything else that makes their deadline-heavy industry function.

But if you tell someone at OP's modernization group that due to incomplete information you think that the 30-minute task to change the text of that button will take "no more than 3 weeks and $8,000" they'll laugh you out the door. Optimistic estimates get rewarded, pessimistic estimates get discouraged, accurate estimates are irrelevant, and in the end you're constantly behind schedule and no one's really surprised.

Unfortunately it’s often true. People keep saying: "but didn’t you initially say X?"

"Sure I did, but I have new knowledge" won't always work.

A nasty side-effect is that people who are aware of this shy away from giving you numbers.