> Who is going to pay for all that power if none of the consumers are?
The consumers of course, that is assuming the grid uses an hourly rate. When all those roof top solar arrays push power into the grid the price goes down, possibly even below zero - you'd have to pay to push power into the grid and "get paid" [1] to consume power - if the grid is close to capacity. During the night they draw power from the grid and pay the hourly rate which may be - but does not have to be - higher than the rates paid when the sun was up.
What if the grid gets more power in during the day than can be delivered to customers? They can use it to charge their "grid-scale" battery which they use during the peak hours in the evening when everyone comes home, turns on whatever power-hungry devices they have. That battery will save them a lot of money compared to the gas-turbine peak power plant they'd otherwise have to use.
In a hypothetical situation where everyone has enough solar capacity installed to cover their own needs it will be more efficient to have those batteries installed as close as possible to where the power is needed, i.e. in individual homes or possibly at local transformer stations. I don't think they're there yet nor will they ever be able to get there in urban environments with largely multi-storied buildings.