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There are two answers to this.
The first is what everyone says is that it is to protect grid workers from being zapped by power backfed from solar to the grid which is true and a good enough reason for shutdown but in practice I think it is mostly a marketing excuse. A grid tied inverter is literally connected to the grid. I needs to sync to grid frequency and output a voltage just a tiny bit above grid voltage to be able to push power out. If the grid is down then there is nothing to phase lock to so the inverter just cannot export anything as it has nothing to work with.
A grid tied inverter cannot run your house during a power cut as it directly connects to the mains so either it shuts down or tries to power the entire local grid which is clearly impossible unless you have a solar farm and even then the frequency locking would make this very problematic.
Summary – a grid tied inverter really has no option apart from shutting down in a power cut but even if it had some fancy electronics to allow it to create a local grid phase it would be trying to power the entire area or possibly the entire country so it is pointless to try.