The premise is false.
You can make class B or Class AB amplifiers without emitter followers; indeed that was the norm for at least the first thirty to forty years.
Here's a counter-example.
simulate this circuit – Schematic created using CircuitLab
This is only a representative, with bias details and overall negative feedback omitted, but it is a classic example of a Class AB or Class B amplifier, depending on the voltage applied at Vbias.
Older engineers may laugh to see it drawn with transistors, but (a) Circuitlab, inexcusably, doesn't offer valves, and (b) this is actually the way early transistor amplifiers were built (usually with PNP transistors, since NPN Germanium transistors were rare beasts) when transistors were new and this topology was familiar. So you will find it in 1960s transistor radios, identifiable by the output transformer.
Q1 and Q2 are the output devices, both in common emitter configuration. (It would be common practice to add small emitter resistors for better current control, bypassed with large capacitors. This matches "automatic bias" in valve circuits, where Vbias would then be 0V).
With Vbias up to 0.6V this is Class B, with some element of crossover distortion : above 0.7V it's into AB, and above 0.7V plus (Vin peak * Q4 gain) pure class A.
Q3 is a phase splitter : Q1 is driven by its emitter follower output (gain = 1) while Q2 is driven by its common emitter output with gain = -R1/R = -1. (Approximately; I did say I was omitting details).
Another common phase splitter used a long tailed pair input stage as seen in most opamps, providing both true and inverted outputs.
Q4 is the main voltage gain stage though the output pair also provide voltage gain.
The reason this configuration fell into disuse is obvious : the output transformer. But feel free to invent transformerless configurations (perhaps based around full bridges) if you like; just don't blame us fi it turns out to be more difficult than at first glance.
The basic circuit configuration lives on where transformers are unavoidable; typically in cheap 12V to mains voltage inverters, with MOSFETs, and either square wave drive, or PWM drive to produce a "pure" sinewave.