Yeah, I think it really helps to think about the grid as basically one giant spinning machine. Everything is connected with wires instead of driveshafts, obviously, but a low frequency means that all of those machines that are burning fuel to try to spin at the right speed can’t generate enough torque to spin the rest of the machine at the right speed. And on the other side, spinning too fast means that all of the machines are burning too much fuel and need to slow the heck down right now (which can be hard to do with, for example, nuclear).
That's the point though? The generator can't be lower or higher frequency than the grid. It can be applying its maximum power into a grid that is still short of power, which is probably a better situation than if it was not doing that. Tripping a generator that is supplying power into a grid with too much power (frequency too high) at least makes logical sense. Shutting down generators on a grid with too little power (too low frequency) makes no sense, unless the generator itself risks damage. Loads should be tripped offline when there's too little power, not generators.
One of the parent posts correctly identified there are thermal issues with operating at significantly off nominal frequencies for extended time periods. System operators will specify frequency bands and minimum time a generator has to stay online for each band. For example we have to stay online indefinitely for frequencies 58.5 to 61 Hz, and can trip after 60 seconds for 57.5 to 58.5 Hz, and can trip instantly below 57.5 Hz.
Some plants the system operator has the ability to send a signal to instantly open the generator breakers to shed generation if necessary.
>> It can be applying its maximum power into a grid that is still short of power, which is probably a better situation than if it was not doing that.
> One of the parent posts correctly identified there are thermal issues with operating at significantly off nominal frequencies for extended time periods
Yeah, that's very much the problem. Power sources that burn fuel to generate electricity generally don't like being run at 100% throttle for long periods of time. In a low frequency situation you've got potentially multiple countries of generators all running flat out trying to get the frequency back to where it's supposed to be. If they reduce throttle without having something else come online to take the place of the energy they were producing, the line frequency drops further.
Nuclear has its own issue with running full throttle: once a plant has been running at 100%, it takes time for it to throttle back down and might not be possible to immediately throttle back up. There's decay heat from the fission products and there's short-ish lived (up to 40-50 hours though) neutron poisons.