Coax is half-duplex too
No, it's not.
With proper impedance matching networks and reasonable termination at the ends of a run you can send separate signals at the same frequency/band of frequencies down a cable in each direction. (Impedance discontinuities DO reflect some of the signal going one way back the other way, causing some interference. But even that can be "tuned out" by suitable corrections if it's too severe to just ignore.)
You can do it on a balanced pair, too. Telephones have done this with audio for more than a century, and I recall encountering a simple hack to do it all the way down to DC back in the days of discrete-transistor logic. (And it has nothing to do with two wires being involved, either. With N (= any power of 2) conductors and "phantoming" you can have up to N-1 balanced and one unbalanced two-way transmission lines on N wires.
Time Domain Reflectometry does this to FIND and MEASURE discontinuities in a cable, essentially firing a pulse down the cable and listening to the reflections, radar-style.