As it is provisioned for peak demand, the grid will cost roughly the same to maintain as it does today, even if people only use it 10 days a year. In this world, there aren't many options:
1. Charge a fixed fee to everyone hooked up to cover the cost of maintenance and repair (and servicing any bonds).
2. Don't charge a fixed fee, but increase the electricy rate by 36x (365/10) so the overall income is the same as before. This will bankrupt those few folks who can't afford their own solar-battery system (or don't have sunlight reaching their rooftop).
3. Have the government maintain the grid and generation infrastructure, similar to roads. This is very similar to option 1 (especially the means-tested version of #1), except the money is collected via taxes instead of a bill from the utility.
4. Let the grid fail by not maintaining it. Everyone must maintain their own self-generation infrastructure, with no economies of scale.
I don't think options 2 or 4 are wise...