I don't know why that would be the case. Why would we build nuclear plants that produce too much power when we could build the amount that just produces a certain portion of our power and that can run wide open so that no excess need be sold off. France just put too much of its power generation in a non-flexible energy source. If it had only build enough for 50% of its power, it probably would not have a problem.
They made it sound like that, but I don't believe it. I always thought that the fuel costs were minimal and that the real cost of operating a Nuclear plant was the cost of compliance with regulations and up front cost of the facility which also has a lot of compliance load to it. Both of those go down the more you do them. And the more the public is open to the plants.
I think your parade is about an elephant and a clown short of a real parade.
You could simply use the excess power at off peak times to pressurize huge turbines with compressed air. Then during peak times you draw off this available stored energy. It doesn’t take a rocket scientist to solve this problem. Anyone raising this as an issue is hard core anti-nuke.