Your numbers are not quite accurate. A real world example in the suggests more like $7.5B / Gw for a new nuclear plant and a whopping total of $27B. Gigafactory

Your numbers are not quite accurate. A real world example in the suggests more like $7.5B / Gw for a new nuclear plant and a whopping total of $27B. Gigafactory construction was finished after two years. A nuclear power plant takes at least a decade in practice. So right now that leaves $22B for producing batteries and solar power/wind. The latter costs about $.3/W So $1B gives you 3GW of peak power. You can have ten time the output and produce batteries for $12B over eight years before the nuclear power plant even starts production.