alt Hacker NewsThere are agile methods that forgo estimates and deadlines though
This is what "agile" is: https://agilemanifesto.org/
More specific methodologies that say they are agile may use concepts like estimates (story points or time or whatever), but even with Scrum I've never run into a Scrum-imposed "deadline". In Scrum the sprint ends, yes, but sprints often end without hitting all the sprint goals and that, in conjunction with whatever you were able to deliver, just informs your backlog for the next sprint.
Real "hard" deadlines are usually imposed by the business stakeholders. But with agile methods the thing they try to do most of all isn't manage deadlines, but maximize pace at which you can understand and solve a relevant business problem. That can often be just as well done by iteratively shipping and adjusting at high velocity, but without a lot of time spent on estimates or calendar management.
Yes, people keep linking to the agile manifesto as if it's some sort of amulet protecting software developers from any sort of accountability or responsibility for their work product in a professional setting.
It seems like you acknowledge some amount of estimating is needed and I agree that there is an overemphasis on estimation in many places, but I'll ask you the same thing I asked others, which is:
How do you do either of the following without spending any time at all on estimates?
"Deliver working software frequently, from a couple of weeks to a couple of months, with a preference to the shorter timescale."
"At regular intervals, the team reflects on how to become more effective, then tunes and adjusts its behavior accordingly."