Cost of nuclear power - it's all in the margins
I think the bit missed here is called a "marginal cost". That's the EXTRA cost of producing one more Watt from any point. For nuclear, it is almost zero. In essence you insert a fuel rod a little more, and watch a gauge. Nuclear fuel is "used" whether it's generating electricity or not, the decay just happens. Physics is like that. In other words it costs roughly the same to have the thing sitting idle as it does to be generating on full whack.
Consider a coal plant. If it is not being used, it's very cheap. You have to pay for labour and whatever fuel is needed to keep it ticking over. Once it needs to be used every Watt it generates needs a shovel (or whatever) of coal thrown in. The cost of the extra Watt is Very High Indeed. If a “shovel of coal” costs £1, and you sell electricity for £1.20 per “shovel equivalent” (I’ll call it a Watt to make life simple) you make a marginal profit of 20p per Watt sold. It’s not that simple though, because you have to pay all those fixed costs. Imagine they are £1million per year. To cover the costs you have to sell £1million divided by £0.20 Watts = 5 million Watts. After that, every extra Watt makes you 20p.
Now back to Nuclear. The fixed costs are higher, so let’s say £2million. Each Watt costs 1p to generate (remember, the fuel is a fixed cost, and in that £2million). So each Watt we sell makes us £1.19. We have to sell £2M/£1.19 or about 1.7million Watts to reach break even. After that, each Watt we sell makes us £1.19. At 5million Watts, where coal breaks even, we have made 3.3million Watts times £1.19 or nearly £4,000,000. Those numbers are made up, but demonstrate the point of why it’s cheap. The tipping point will be at a very different point in reality, but there will be one.
Having high fixed costs is economically risky. If there was no demand then the nuclear plant would have a £2million loss, the coal plant £1million. So the secret is to keep nuclear plants as busy as you can, selling as much electricity as you can. Enter the Interconnectors. These are links between grids, such as between France and the UK. It is almost exclusively pulling (or pushing, I dunno) electricity FROM France TO the UK, not the other way. Why? Well, it’s cheap for France to generate extra Watts to help us out, so it makes lots of money doing it. Going the other way, we with out unpredictable wind and marginally expensive coal plants can’t compete with France, so we don’t tend to sell that way. Unless there is some disaster in France or elsewhere in mainland Europe, and they need all the power they can get. This, by the way, also helps out the French tax payer and the French nukes in keeping French prices down.
That's the nuclear model, that's why it's so cheap - IT'S THE MARGINAL COST OF PRODUCTION, that far, far outweighs the hidden costs you refer to, especially as all energy sources have subsidies, and the costs of nuclear waste storage are not as expensive as you would think, in the context of the sums one is considering for power generation for a whole country.