[twblalock]

My advice is to view this as an opportunity to improve the company's Jira workflow.

The status quo of issue tracking on your team is not scalable. And it's entirely reasonable that management should have a way to track your work. You are a small team in a big company and you're going to end up using whatever issue tracker everyone else uses.

You say that your team works better than others in the company. Tell management how your team's processes have resulted in high productivity and suggest improvements that other teams can benefit from. If using Jira hurts your team's productivity, find a way to quantify that -- ideally in terms of how the capex is higher than it needs to be because developers are wasting their time.

Recommend small, incremental changes rather than remodeling the entire system, and get other engineering teams on board with your proposals -- if the processes are bad, other teams are likely to want change too.