You are incorrect in how a nuclear power plant is operated. It can be throttled back, just not quickly without problems. Also electric utilities tend to keep the nuclear plants fully loaded and shut down and/or lower other plants during lower demand times.
I was oversimplifying, of course.
It is not economical to throttle a nuclear plant up and down due to grid demand, as you’ve noticed. Thing is, if we build more nukes (as we need to), then we’ll end up with surplus power at night that could (and should) be used for other things.