If the power from the solar system can be put on the grid at all it has to be converted from DC to AC, and that means you should be able to use that power as needed for your home and not connected to the grid while the sun shines.
The inverters need to synchronize with the AC on the power lines, otherwise if they are out of phase or off frequency they fight the grid power, to the detriment of everyone involved.
No 60Hz form the grid, no ability to run.
A local 60Hz oscillator and a bunch of electronics to disconnect from the mains during an outage, with detection of reestablishment of grid power, and re-synchronizing before reconnecting would solve that problem, but would increase system complexity and cost. Worse, a failure in any house's system could charge the lines and potentially electrocute repair workers who are patching known (as far as all their switches say) un-powered lines.