Not only as a safety feature but as an inherent part of their design: they are designed to produce AC that's in sync with the grid. Same frequency and peaks/valleys as the same time. In a blackout there is no grid to follow, so the inverter shuts off.

By design, sure, but it's not a fundamental limitation. There are inverters that do not shut down when the grid signal is lost, and will resync when it comes back up.

It is also interesting to read up how this plays into black start plans for the european power grid. You would think solar parks make black starts ... "easy" - just turn them on and have some power, but due to the inverter functions, that's not the case.

Instead, one of the plans I've read about has to start a few black start capable power-plants first to get some kind of phase into the grid. Then you can bring consumers and solar parks online until there is enough load on the grid to bring up larger power plants, while the quick-reacting solar parks are taken online and offline to balance the grid so it never has too much or too little load on it.