About 10 years ago I had a chance to work in the Utilities vertical for a power producer. I asked the same question: how is the frequency set and the answer was that the biggest power plant sets the frequency because they can produce a lot power and any other smaller generator would not be powerful enough to change the frequency.
Sure, the smaller plant gets pulled into the larger plant's inertia.
However, DC-AC converters don't have an inherent inertia. They can follow almost any frequency and phase within reason. Certainly a DC-AC converter should be able to respond way faster than any frequency/phase changes that a mechanical system can generate.
In theory, they should be able to set themselves to be ever so slightly closer to ideal so that the amount of power they have to sink is limited but are still exerting a very slight force to bring the grid back into compliance rather than continuing to add load which propagates the collapse.
