Thinking about this makes me wonder how all real world power plants aren't designed to survive a grid outage? Why would you ever need to black start a real power plant? Like, can't you design it so that it disengages from the grid rather than shutting down in a catastrophic outage like this? Or make it only take on a fraction of the load or something?
The problem is that it's still steam pushing spinning rust. You can't instantly scale up or down, let alone do so in an organized fashion. If you were happily generating 1000MW out of 1500MW max, there's very little you can do if a power line goes offline and you're suddenly connected to 2000MW of load - or only 250MW. At best it's going to take tens of seconds to adjust, which in practice means you're forced to dump the entire load because in the meantime your output has deviated so much that you're causing serious damage to downstream equipment - or your own. And load shedding isn't really an option because you're now operating as an island, which means you have to instantly figure out how the grid is now connected, what the current supply/demand is, which neighborhoods should be turned off to best match the pre-incident demand, and what the impact on the local grid is - there are way too many variables there to be able to respond in a fraction of a second.
Starting back up from zero is significantly easier, as you are completely isolated and have zero load. You turn the power plant on, and start slowly adding local load to ramp up. Synchronize with neighboring plants where possible to build the grid back up. The only issue is that a power plant needs a significant amount of power to operate, so you need something to provide power before you can generate power. In most cases you can just piggyback off the grid, but in an isolated black start it means you need a beefy local independent generator setup. That costs money and it's rarely needed, so only a few designated black start plants have them, paid for by the grid as a whole.
Disengage from the grid and do what with the vast amount of power that suddenly has no place to go? That kind of power tends to break things. Powerplants have big cooling towers because disposing of heat is problematic.
And you're assuming that there is a throttle setting that lets the plant produce so little power that it only runs itself. Think of the Falcon 9--the landing is hairy because it's impossible for it to produce less thrust than it weighs. The engine will go out if you try to throttle it too much.
