Driving can push up the low points (charge cars overnight), but heating would put a lot of demand in winter months, meaning a day time cold day in January with no wind will require a lot of dispatchable electricity, at night time in September with a gale blowing wind will be providing almost all the demand.

Nuclear doesn't really help as it's more expensive than the wind when it's windy and demand is low, and its impossible to build enough to cover the peak January demand unless you spread the fixed cost over the entire year, which means getting rid of every other form of electric production, and you'd still end up paying more per kWh than you would with other forms of storage.

Nuclear can't survive in a free market. It can't scale up to provide for areas of high demand, low supply, and it can't scale down to be affordable when there's high supply and low demand.