How could you (in theory) run an induction cooker from a DC supply?
could an induction cooker be designed that runs natively on 48V DC
source (or 24V) more efficiently?

A simple block diagram suggests that it can run from DC: -

Picture from here.
At the top left is the incoming AC that is bridge rectified and filtered to provide a DC bus for the main power circuits of the cooker. The bridge rectifier and filter will have losses so, if those are bypassed by using a DC supply that suits the bus voltage then the solution would be more efficient.
Can it be made to work from 48 volts or 24 volts? 

The higher voltage is better because the current would be less for a given power and cable losses would therefore be less. But remember, the coil in the element would need redesigning to suit a lower DC bus voltage because on AC cookers, the bus voltage is going to be roughly in the range 140 volts DC and 350 volts DC (suiting an AC line voltage range of 100 volts RMS to 240 volts RMS). It's doable.