Storage could be a solution for sure. Compressed air has been discussed, and I think there are a couple real examples. There's a Wikipedia article on it. A couple projects are mentioned in the History section. The issue I understand with compressed air is heat. It gets hot when compressed, and that heat energy is lost. Then when decompressed, heat needs to be added. In a way, storage can be thought of as generation capacity. The system today works on intermittent energy supply (e.g. coal train deliveries a few times a week) that can be stored (pile of coal) and converted to electric energy on demand (by burning it in a boiler). Doing the same with wind or solar (intermittent energy supply), pumped into storage (whether air, batteries or hydro dams) and converted on demand (storage output) essentially provides the same functionality.
I guess my implied intent is to reduce the impact of our power generation on the environment. If a majority of homes had solar panels trickling energy into the grid, and the utility then stored that extra power for later use, the need for coal drops. That eliminates transport costs, environmental damage from mining and burning, etc, etc, etc.
That can work on paper, and the technology exists to do it (compressed air, pumped hydro, batteries). The challenge is the cost. It's surprisingly cheap to dig up coal and burn it for energy. There are a million terrible side effects of fossil fuels, but faced with them consumers almost exclusively will pick the cheaper option.
As long as the general public continues to pay for all the side effects of the "cheaper" option. It's only "cheaper" because the majority of the costs are subsidized by the public. Make coal producers pay for the FULL cost of the product - probably with a carbon tax - and I think the math pencils out very differently.