The issue is that the Finance dept will show up and ask why you chose the more expensive insurance. Sure, if you're able to show how much the annoyances of the cheaper company would cost you, they'd probably shut it. But I'd argue it's not that easy. Plus, all these annoyances aren't borne by the security team, so they don't care that much in the end.
My first thought might be to put together a report showing the cost that the cheaper insurance would impose upon the organization which the more expensive up-front option is saving you. Perhaps even serve that up as a cost-savings the finance department is free to then take credit for, I'unno. :P