Then, most transistors that would do high voltages had terrible Hfe – so the common emitter input id the current gain and biased the HV-but-otherwise-crappy output transistor. And yes, of course ...

Just as the common emitter amplifier and common base amplifier each tied those respective transistor terminals to a fixed potential and used the other two terminals as amplifier input and output ...

Off-line flyback uses HV transistor in common-base configuration; LED-driver level-shifter includes fault detection; Cascode MOSFET increases boost regulator’s input- and output-voltage ranges; ...