The thing is, coal has been used for baseload, which is horrible. Coal produces around twice as much carbon per unit heat as natural gas, and baseload generation runs 24/7.
Use nuclear for baseload and solar for daytime demand and even without any storage technology, you limit the need for generation from fossil fuels to the high demand period in the evening after the sun goes down. Then add in demand-based pricing to load shift anything that can be (like charging electric vehicles) into the solar generation period.
Going from burning coal 24/7 to a couple hours of burning natural gas in the evening is a huge reduction in carbon emissions.
At that point it's a question of economics. Alternatives exist -- synthetic fuels produced in the daytime with energy from solar generation and then burned at night, biofuels, etc. They're not used because they're more expensive; impose a carbon tax and maybe they're not.
And that's assuming no one comes up with anything creative. Here's an idea -- run a nuclear reactor 24/7 equipped with thermal storage. Then you can store the heat from the reactor during the day when you can get cheap electricity from solar, then use the stored heat to satisfy the few hours of peak demand in the evening after the sun goes down, then generate electricity directly from the reactor for the rest of the night until the sun comes up.