The mode of SSB is alive and well. It has relevance for long-distance comms and does not waste spectrum. The orthodox methods of generation are Filter, Phasing and Weaver. These methods can be and are done in DSP or firmware but the fundamentals are the same. The resulting low-level analog RF signal goes to a linear amp possibly via one or more hetrodyning stages. The linear amp has not gotten much more efficient since the 1960s. So the more efficient classes of PA operation are not utilised in practical SSB rigs. Example FM and its digital cousin FSK are fine running class C or the less-documented class E. It has been said that it's mathematically possible to apply AM and FM to a RF carrier simultaneously to make SSB.
The Amateur who said this may be very very old now. When he was in his heyday it would not have been practical but the question is: Can we do this now?