It's nice to have a headset on your desk telephone, for handsfree conversations. A number of phones have a headset jack, either of the submini plug used by cell phones, or using a phone handset jack. Many companies buy headset units that plug into the handset line to provide a headset, some of them are even wireless.
But bluetooth headsets today are cheap, standardized and have a competitive market. And they are of course wireless. Many people already have them for their cell phone. I have seen a very small number of desk phones support having a bluetooth headset, and that shouldn't be al that expensive, but it's rare and only on high-end phones.
Here's the idea: Put bluetooth headset support into the PBX. Bluetooth headsets can't dial, they can effectively only go on-hook and off-hook with a single button. You would associate (in the PBX) your bluetooth headset with your desk phone. A bluetooth master would be not too far from your desk, and tied into the PBX, or into a PC that talks to the PBX. When your BT headset was in range of this master, it would be tied to ith with Bluetooth. (You would have to do an actual bluetooth pairing in advance. In addition, many people have bluetooth headsets normally linked to their cell phone, and call attempts from the headset go to the cell phone. The system would have to switch that over to the PBX.)