This was in the days before frequency dividers and phase locked loops. Such systems also had a certain amount of inherent time delay in the frequency correction system, which meant that frequency errors would persist for a while before they were corrected. The other way to produce FM, which was more commonly used, was to produce phase modulation instead of frequency modulation. Phase modulators, unlike frequency modulators, could be used with unmodulated carriers provided by crystal oscillators. Phase modulation and frequency modulation are close cousins.
Frequency modulation is the rate of phase modulation.
In other words, the amount of frequency modulation is the time derivative of the phase modulation. In a phase modulation transmitter, as the modulating frequency is increased, the phase modulation stays the same but the frequency modulation increases. In a frequency modulation transmitter, as the modulating frequency is increased, the amount of frequency modulation stays the same, but the phase modulation decreases. This means that FM and PM are really the same thing except for a frequency response issue. So, by applying a 6 dB per octave descending slope to the audio frequency response, FM could be produced by a phase modulator.