Do you think, getting flooded is a direct result of using Jira or is it related to the way the project is structured? Getting flooded is always a bad thing (and probably your PM should get annoyed by that), but I believe that could happen to you with any other tool.
Jira's a variable, for sure, but it's mostly management.
Mainly, Jira metrics are what run our management (actual HR managers, not PMs). Because of needing set qualitative measures to judge teams on, no one is allowed to use anything other than the Approved Jira Workflow For Scrum Teams.
My team is over 50 sprints in with a fleshed out backlog... there's no reason other than politics for why we can't go Kanban. And Kanban is pretty much the only way to stop that flood since more things can ebb and flow naturally rather than in structured time frames. The alternative would be to make stories ultra tiny to get the burndown started earlier, but that would cause a dramatic drop in effectiveness since we'd be bogged down with the process of it all.
While Jira does have Kanban boards, the concept of something not being done by the end of a sprint is too ingrained in how teams are deemed successful or not.
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