I remember seeing an old radio with slug tuning and two seperate inductors were slug-tuned in-tandem. I'm guessing here but that possibly performed the function of input tuning and local oscillator tuning thus keeping the LO 455kHz away from the desired radio channel. I know that dual variable caps were often used for the same purpose but given the physical size of variable caps for AM broadcast bands I think ferrite slug tuning would win-out.
I would also consider that tooling up for ferrite slugs and coils is simpler and, if design adjustments needed to be made, a few turns added or removed would be simpler than altering the plates of the capacitor. Different ferrite slugs gives yet another option over caps.
I also remember the push-button pre-select tuning on car radios - although the mechanism was a little tortuous on ferrite tuners (the "system" mechancially memorized the slug position), I'm struggling to visualize how this would work with variable caps (which of course rely on rotation of the interleaved plates).
I'm also pondering the prospect of (say) 3 or 4 slugs operating in tandem negating the need for a local oscillator, mixer and IF strip because the RF selectivity would probably be good-enough to funtion as a half-decent AM radio.
EDIT A day later and I've thought of yet another advantage - tuning across a band of frequencies for the desired channel is OK but for either a variable cap or variable inductor tuning, the Q of the resonance changes from one end of the dial to the other. I can imagine that if the ferrite slug introduced into the winding was low loss (on introducing the slug) and gradually got "lossier" along its length, as inductance rose (and selection frequency dropped), the Q of the circuit could be maintained flat (or nearly flat).