Looking at the patents:
SU890 (Russia, filing date 06/23/1921) – oscillator without a linearizing coil,
US1661058A (USA, filing date 12/05/1925) – oscillator without a linearizing coil.
In RCA and custom theremins for Clara and Lucie, the linearizing coil is already present.
It would be interesting to know when and under what circumstances Lev Thermen came up with this idea. In principle, it seems to merit its own separate patent.