"Maybe somebody like peter H. could shed light on this"
A LOT of work has been done on transient models for synchronous three-phase machines.
A lot of work has been done on induction machines, too.
However, little work has been done on modeling machines of the RPC type, where induction within the two real phases is transferred to the one manufactured phase across the squirrel cage rotor.
I can state with reasonable certainty that "slip" is an important factor, and, within reason, the more slip, the more power which can be transferred, and that with zero slip, essentially zero power is being transferred.
However, slip can be a bad thing, particularly if it exceeds 90 electrical degrees, a violation of the so-called "equal area criteria", whereupon the system becomes unstable, perhaps for a cycle or two, or possibly for an extended period.
Ideally, one wants the RPC system to be reasonably stiff, yet flexible enough to respond to significant changes in load, without violating the stability criteria.
Having no load at all on the rotor, save windage losses, presents one extreme.
Having a substantially immovable load on the rotor, say, as a consequence of a very large flywheel, presents another extreme.
Pole-slipping cannot occur in the first case, but is almost guaranteed to occur in the second case.
So, as is usually the case of these empirically designed systems, one performs some experiments, and then settles on that case which appears to work best.
My intuition says that adding a reasonably sized flywheel can improve transient response in some cases, but not in all cases, and for each case where such a reasonably sized flywheel results in an improvement, a more significant improvement is possible by eliminating the flywheel altogether and increasing the size of the idler.