I got myself a plastic welder - the thing that melts little pieces of metal to strengthen plastic joints - now I can keep old plastic things in shape almost indefinitely. Cost like 10 usd or so and has prolonged the life of all manner of things.

If you still want to make the old headphones work these welders are a godsend, and with some small amount of diy work of cleaning, sanding and buffing you can easily hide these welds.

I personally like to leave them though since they accent that something that was once broken is whole again, and that it has a long history!