However, the final part has nothing to do with jira IMO. You would have the same behavior in these organizations regardless of tool.
The dysfunction you describe goes way beyond a single or set of tools.
It wasn't atlassian that "came along" - someone penned down an agreement and, from what it sounds, there was a lack of clarity both in regards to current and future principles of work and collaboration.
What we can do, as devs, to protect ourselves from the madness you describe is to be explicit about our work processes and their purpose. Nothing much, but just a set of agreed upon principles and ways of working which should have nothing to do with tools.
What you end up with, by being explicit, is for having "something" to be supported by one or several tools.
Makes it easier to evaluate, select and change tooling that is fit for purpose.
So yeah, I have found that the tool shapes the process, not the other way around.
It would probably work the other way around if every organisation built their own project management tooling around their own processes. But that would be insane.
then they get promoted, and may never learn / experience why a task / defect tracker is not where you store requirements / design.
(note: the above comments are for long lived software only. it you rewrite your web site from first principles every you, do whatever. it doesn't matter)