IANAEE (not an electrical engineer), but doesn't a gas turbine spin at a constant speed to drive a 60Hz generator, regardless of whether it's running at 20%, 60%, or 100% of capacity?
When there’s a load imbalance on the grid (more load than capacity), the turbines physically slow down as inertial energy is extracted from them. This causes the grid frequency to drop. It takes some time to ramp up production and speed up the turbine etc.
The maximum slow-down of the turbines (before the generator trips off-line, removing the load on it) is far less than you seem to assume. The article's graph shows the 60.00Hz grid frequency dropping...all the way to 59.92Hz. That's 0.1333%.
For an on-line gas turbine, the time to ramp up production is the second or few needed for the automated controls to open the throttle on the "Gas IN" pipe. It's basically a natural gas-burning turboprop jet engine, with the propeller replaced by a generator. (Yes, this can be less efficient in a combined cycle plant.)
The more interesting thing about rotating power plants is that they are routinely destroyed by transmission outages, because when a rotating generator is suddenly disconnected from its load, there are infinity terms in the equations that govern its motion and infinity isn't a thing you can resist. For steam turbines the control system has to slam the valve shut on the steam, otherwise the machine would overspeed, and closing that valve destroys some sacrificial part of the steam plumbing (hopefully). Steam power plants have to be inspected and repaired after disconnects and this is one of the numerous reasons why fission kinda sucks on the reliability front.
While the infinity terms may be a useful way to think about how the system loses stability, I think it's better to think of it in terms of energy: at any given time there's some amount of energy that's been injected into the system in the form of hot gas which hasn't been converted yet. Even a few seconds worth is a lot of energy, and if the electrical load is removed, that energy has to go somewhere.
An SD40 locomotive can dissipate about 500kW that way, so you would need the equivalent of 2000 locomotives worth of resistors and fans to sink the 1 or 2GW or more that a fission power station produces.
This is true only if the protection does not operate as designed. They are NOT routinely destroyed by transmission outages. You have been misinformed. Rotating machines cannot overspeed instantly, as they have inertia.