Most of a nuke plants' cost is in construction, but that is not because its operating cost is low. It is just insanely expensive to build. Then, its operating cost is high. Each moment it is not producing at 100% rated power, its per-kWh cost increases accordingly. Its operating cost does not decrease proportionally when it operates at below rated maximum power, so the operating cost per kWh is multiplied by the difference. And, operating at below rated capacity, the construction cost is amortized over fewer kWh, again making the per kWh cost greater.
You already well understood all of the above, but evidently hope readers will not.