But those other kind of power plants are okay to stay off and start only when such situations arise, right? Still good for the environment I guess - you only burn fossils when the network restarts, which will probably only happen every few years in some corner of the continent. If I understood it correctly, that is.
The issue with solar and wind is that when they're being initiated in the project stage, they're advertised as the equivalent of some amount of average power (or even maximum power, if the project initiators want to be disingenuous about it), when the required amount of construction to match baseload capacity would easily be 3-4x that number.
There really is no one-size-fits-all solution, except for having an energy mix of renewables, with existing thermal power on standby.
Which is basically every winter in Northern Europe at least, and is usually when electricity demand is the highest (very cold days tend to have the least wind).
The UK was very very close to a blackout last winter for this exact reason. If Denmark weren't able to suspend maintenance on part of their grid to max out the Viking HVDC (it was running at half capacity) there would have been loss of supply. Potentially contained to one region and temporarily but it's hard to say for sure.
What's worse is the communication from NESO (now government owned, very recently) was downright misleading to how close it came.