I addressed the rest elsewhere, but done well a lack of estimates makes people more accountable. If I am shipping something every week (or as is common for my teams, more often), stakeholders can directly evaluate progress. There's no snowing them with paperwork and claims of progress against semi-fictional documents. They see what they see, they try it out, they watch people use it.
The reality of use is what we in software are ultimately accountable to, and that's what I am suggesting people optimize for. Closing that feedback loop early and often builds stakeholder trust such that they stop asking for elaborate fantasy plans and estimates.
You replied to me in like 10 different places, nearly all of which are in responses to posts that weren't directed at you, so I'm trying not to fragment this discussion too much.
I will ask this here: If you are shipping code to production on a weekly basis, is that not a schedule, also known as a deadline for delivery?
If you expect to ship code to production every week, how do you know whether there will be something to ship without doing any estimation of the effort and time required?