I'm not really seeing what you are getting at here.
So it seems!
Folks are constantly diddling with greater or lesser capacitance to try to hit the best performance, "generated leg", when, of course, the load ON a given load-motor is changing, or which one or which combination of several possible loads is a dynamic.
Directly variable capacitance is cumbersome, but it is not the only means of introducing a controlled dynamic to the same effect.
Only the one leg needs it. The "package" could be less costly in large HP than high-powered VFD or Phase-Perfect, and more robust, also "fail-safe", than either.
A controlled reactance and some dirty-beach sand - it could perhaps be automagicated, yah?
Phase-Perfect's big inductors don't rotate. The rest of the 'tronics might be cheaper and simpler if they
did do, high HP especially, given 3-P motors are mass-produced at such high volumes and sharply competitive pricing...
Challenge in there for a younger person?
Or for an older one to dust-off fossilized experimental data?