There have been lots of radio sets (military for sure) that have ISB, Independent SideBand, transmission or reception but not in the full duplex mode. As others have said much too difficult and expensive to obtain full duplex on a single frequency.
The PMG's Dept (later Telecom Aust),used ISB extensively for long haul HF comms,in the '50s,'60s & into the '70s.
They had separate transmit & receive Carrier frequencies,as well as separate Tx & Rx sites.
They thus had both frequency & geographical separation,
.
That said,some of the systems were really Simplex,using VODAS/VOGAD devices,which operated on the users voice,so as to not need PTT.
I think the Perth-Melbourne system was full Duplex,though,as the distance between attended Rx & Tx sites could be made much larger in the cities,than the semi-unattended sites in remote towns.
If you are a Communications carrier,it makes more sense to be able to use the two sidebands for different conversations.
If you use the other sideband for the receive side,you can only have one conversation,per system.
To get back to where you were,you then need another Tx,Rx,& a second frequency.
As there was no advantage in to using one frequency allocation,it was easier to use multiple frequencies to begin with.