Initial cost would be higher, but long term cost of Solar is ridiculously cheap.
There is the AAPowerLink project which proposes exactly this. It's a ~20GW solar farm in Australia with battery storage and a 4500km HVDC undersea cable to export power to Singapore. Seems currently in a planning and Project seems to be in a planning and exploration stage with funding not fully secured though.
Also wonder how much kWh batteries one would need for winter heating (generate at day, use at evening). Kinda feel NZ, especially north island should have enough. Over in Eastern Europe you can get recycled batteries for $150/kWh!
In the end, you'll always need a mix of supply. Or simply better insulation and efficient heat pumps rather than wasting electricity on heating at above freezing.
A more viable though still impractical approach is to store energy in rocks underground. Essentially trading the need for a multi km deep borehole for geothermal with the need to provide your own heat.