Nuclear power already produces 10% of the world's electricity [1]. A 100x increase leaves the world with 10 times as much electricity as is needed, all coming from a decarbonized energy source.
Wind and solar are cheap because we don't currently have to even out their intermittency. Take away peaker plants and then intermittent sources become way more challenging. Solar produces energy in a sinusoidal pattern daily, requiring at least 12 hours of storage for truly non-intermittent solar plants. It also fluctuates over the course of the year due to weather and inclination of the Earth [2]. Wind power similarly sees fluctuations over the course of the year [3].
1. https://en.wikipedia.org/wiki/Electricity_generation#Methods...
2. https://www.researchgate.net/figure/Estimated-normalized-mon...
Compare this to nuclear. Let's increase our production levels 100x. Where does that leave us, assuming that it was magically economically acceptable to electricity customers to pay higher prices than necessary. 15 years for 2.2GW is about 150MW/year. 100x would be 15GW/year. That's nowhere close to being where we need for a full energy transition in the US.
Nuclear, if it figures out its huge problems with construction, will be a small player to help with climate change. But in the year 2023, we know the big players: solar, wind, and batteries. There's no more time for anybody else to scale to catch up. Nobody else has a tech that can compete with such fast dropping costs. The numbers and pace of change are hard to compete with.