If indeed there was global warming to the point of rising seas and other absurdities that they spout then the best solution would be the “new, modern, small safe nuclear plant designs” you refer to. But that’s not the play here, to make abundant and cheap energy.
https://www.nuscalepower.com/technology/technology-overview
1. “But that’s not the play here, to make abundant and cheap energy.” It isn’t? Because?
2. Nuscale is not the only design in production or in contention. There are others in the manner of downsizing with also improving safety.