There 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.

It’s Agile philosophically, and how it should be.

But that is rarely how it works. In the dozens of different projects across ten or twelve companies I’ve had insight into, “doing Agile” is analogous with “we have a scrum master, hold stand ups, and schedule iterations” while the simple reality is “Agilefall.”

I can say with some confidence, having been involved in the movement since before the term "Agile" was coined, that it requires neither.

I grant that both of those are common, but that's because the median "Agile" implementation quickly devolved into mini-Waterfall with more hip names.

I missed that part of the manifesto