The problem with shutting down nuclear is that our production costs are pretty steady. When nuclear is replaced with LNG, the cost becomes more fluid, specifically based on the cost of fuel. While it probably costs a dual unit nuclear plant $25-30/MH-hr (I don't remember where I heard those numbers), that cost is pretty constant as our fuel doesn't have huge price variations and the highest cost are the people. Right now, an LNG plant pays around $15-20/MW-hr, however, if the cost of LNG goes up even a little, say due to increased demand from more LNG power plants, that price will jump quickly, that cost then gets passed down to the consumers.
As far as no one building more nuclear, that partially correct. After Vogtle there probably won't be any more of the "current" nuclear plants built, due to the cost and construction time, not accounting for the various approvals. NuScale is designing SMRs, with NRC approval, so we might start seeing those within the next decade or so.
