For us, an accurate delivery date on a 6 month project was mandatory. CX needed it so they could start onboarding high priority customers. Marketing needed it so they could plan advertising collateral and make promises at conventions. Product needed it to understand what the Q3 roadmap should contain. Sales needed it to close deals. I was fortunate to work in a business where I respected the heads of these departments, which believe it or not, should be the norm.
The challenge wasn't estimation - it's quite doable to break a large project down into a series of sprints (basically a sprint / waterfall hybrid). Delays usually came from unexpected sources, like reacting to a must have interruption or critical bugs. Those you cannot estimate for, but you can collaborate on a solution. Trim features, push date, bring in extra help, or crunch. Whatever the decision, making sure to work with the other departments as colaborators was always beneficial.
Estimating in software is very hard, but that's not a good reason to give up on getting better at it
If you're truly creating such unique and valuable software that it is to be compared to the world's engineering megaprojects in its challenge then perhaps it is beyond being beholden to a budget. Who am I to say?
But 99.9% of this industry isn't doing that and should probably be able to estimate their work.