Can We Use CVT on Inductive Load?

A CVT, or Ferroresonnant transformer, works by creating a kind of "tank circuit" in an AC supply that will not vary in the output voltage in the presence of a wide range of input voltages. But it does so at the expense of efficiency and the inability to react to sudden changes in demand.

So to the first issue, putting them on everything will make those devices consume 20-30% more energy without increasing the work performed. In addition, the CVT will consume this extra energy (in the form of heat) regardless of loading, so just being connected will use considerable energy based just on the size of the transformer.

To the second issue (assuming you get past the first), induction motors use a high peak of current to start, and a CVT will inherently clip that which will make the motor take longer to accelerate, if it even can. But unlike a soft starter, the CVT itself is not made to do this so in order to have it survive in an induction motor circuit, the CVT must be significantly over sized. That then comes full circle back to the first issue.

A servo stabilizer is usually just a variable autotransformer, aka "Variac" (for a common brand name) with a servo controller on the rotating member, connected to a sensing and control board that varies the transformer ratio based on changes in the input voltage to maintain a steady output voltage. They usually have no restrictions on the type of load they can be used on, they are just a regular autotransformer in that regard. But their problem is, they are very very expensive.