Think of it this way: if you buy a house, the “operating cost” is fairly small: upkeep and painting, mostly. Does that mean you can buy a house, move out of your apartment, and quit your job, because your cost of living has just dropped a few thousand a month?
No, of course not. Upkeep isn’t the real cost of buying a house. The real cost is the monthly mortgage payment. Unless you were already independently wealthy, you have to keep your job. Sorry.
The cost of energy for a nuclear plant is the cost of paying back the loans. As other forms of power generation get cheaper, those loans stay the same, making it harder and harder for nuclear to compete. As they get squeezed out of the energy market, they have to raise their per-watt prices in order to continuing to service the loans.
Think of it like this. You rent your house to your cousin, who pays you enough to cover the mortgage. But then your cousin finds a sweet deal couch-surfing in the tropics in the summer. He stops paying you for June, July, and August. You can’t get anybody else in your house during that time, so you say, “Sorry dude, you have to pay more for the rest of the year. I’ve got bills to pay.” That works great until your cousin gets tired of your high prices and moves out, and now you’re left with a mortgage to pay and no one renting it.