Magnetic amps were indeed used in the V2 in the control electronics.

But they substantially predate World War II and were once widely deployed and widely understood. The technology goes back to at least the late 19th century. It was used in many of the places where we'd use an amplifier today, like to run signals in a factory where hydraulics are not practical.

They can be quite fast - if the AC supply is well into the 10s of KHz they can reproduce audio range frequencies.

Some of the first electronic radio transmitters were based on the magnetic amplifier. The radio pioneer Reginald Fessenden developed a system using his Alexanderson alternator (a super-high-speed AC generator) which produced high power (many kilowatts) of AC at the target carrier frequency of around 30 kHz. He then fed the output of that, through a large magnetic amplifier, governing the kilowatts of generator output, with a small control current from a switch or microphone -- amplitude modulation. That was c. 1916.