One good reason for seperate coils is due to the interwinding capacitance - Effectively, every coil (inductor) is non-ideal - they have series resistance and a parrallel capacitance sumply as a byproduct of wire resistance and capacitive coupling between windings ..
The inductance and capacitance in parrallel form a resonant (tuned) circuit, and one wants this natural resonant frequency to be much higher than the frequency you are operating the theremins oscillator at - Also, even if the self-resonant frequency is higher, one wants the capacitance to be as low as possible, because (for one thing) this capacitance reduces 'antenna' sensitivity.
By having smaller inductors wired in series, one can greatly reduce these problems - Big inductors tend to have lower self-resonant frequencies (higher capacitance) - buliding bigger inductors by wiring small inductors together in series greatly reduces the total capacitance 'seen' at the antenna.
Lots of reasons - but in general one wants the inductors to have low capacitance, and this is achieved by having windings seperated from each other (inductors used in theremins are often wound with several seperate coils on the former, and the winding is specifically done in a way to minimise capacitance).