"Fuel storage and reprocessing" isn't that much of the cost and a significant proportion of that is compliance costs and extreme safety measures. The pressure vessel is likewise a small minority of the cost.
Industrial control systems are fundamentally sensors, actuators and a computer. None of those is actually that expensive. Nobody should be paying a billion dollars for a valve.
Older reactors have somewhat high operating costs because they're so old, many of them were built more than half a century ago. Newer reactors often have higher costs because of the lack of scale. If you only build one or two of something you have to amortize the development costs over that many units, mistakes that require redoing work are being made for the first time, etc. Build more of them and the unit cost goes down.
Nuclear, inclusive of construction costs: ~$181/MWh, only better than natural gas because no CO2. Nuclear, cost of continuing to operate an existing reactor once it's already built: $31/MWh, basically the cheapest thing on the market, half the cost of continuing to operate an existing natural gas plant (because you need so much less fuel).
What this implies is that if you build a nuclear plant you're going to want to continue operating it for 80 years, and even then you probably want to just modernize it again instead of actually decommissioning it.
The long-term average returns from ordinary investments (e.g. S&P 500) are ~10%/year, implying that even if you require decommissioning to be prefunded (unlike any competing form of power generation), the amount of money you need is less than 0.05% of what the cost will be in 80 years. Adding $500 million in decommissioning costs isn't $500M in net present costs, it's only $250 thousand in net present costs, because you take the $250k and add 80 years worth of interest (1.10^80) which multiplies your starting capital by more than a factor of 2000.
It's really just the construction, and that's in significant part because you have to build more of them to get economies of scale for building them.
Industrial control systems are fundamentally sensors, actuators and a computer. None of those is actually that expensive. Nobody should be paying a billion dollars for a valve.
Older reactors have somewhat high operating costs because they're so old, many of them were built more than half a century ago. Newer reactors often have higher costs because of the lack of scale. If you only build one or two of something you have to amortize the development costs over that many units, mistakes that require redoing work are being made for the first time, etc. Build more of them and the unit cost goes down.