I had an incident once wrt headsets on an international flight as the OP had. I kept mine. But I was told that on flights which land internationally, they are "required" to collect the headsets. On international flights which land in the US, you can keep your headsets and put them in your seatback when you are done. Does this have to do with the turnaround time?

I don't know the veracity of this. Can any FA help out here?