It is your choice of course, but that battery is a safety hazard and could very possibly catch fire at any time. Like on a plane, or in your car. So do you really want to take a chance just to prove a point. I agree it is frustrating and does not seem fair. If you purchase the battery, it is fairly easy to replace it yourself.
Dell support staff likely did not know about the end of the service campaign.
As for continuing to use the system with a swollen battery - you'll find it destroys the palmrest, touchpad and mainboard long before it causes a fire -- so, in exchange for stubbornly refusing to solve a problem, you'll be in the market for a new system - costing you not $200 or so, but a couple of thousand dollars.
You also won't be flying anywhere with the system - there's no way the TSA will permit a system with a swollen battery aboard a plane.