They aren't being added to nuclear powerplants because nuclear powerplants have a wide and controllable dynamic range (they can run higher or lower depending)
Nuclear powerplants, typically, are capital intensive. For this reason, their operators aim for high capacity-factors. Unless economic forces are being ignored, they cannot easily be throttled. They run at 100%, all of the time, except when they are being refueled. The only nation that uses its nuclear powerplants in load-following mode is France -- since such a high proportion, some 80%, of its electricity is nuclear -- and France pays a price for that.
Additionally, it is not mechanically good for a nuclear-powerplant to throttle up and down. Such cycling causes parts to wear-out faster. If it is going to be used at all, it is best to keep it on, at a steady output.
There are other considerations. The nature of reactor poison build-up is such that throttling-up immediately after throttling-down tends, in typical reactor designs, to be difficult to do.
Unlike nuclear-powerplants, hydro and gas-turbine powerplants load-follow well (though the more-efficient gas-turbine powerplants take longer to start-up and might have to burn fuel, idling).
I will confess I know less about fission power plants than you seem to. Good point on the capital intensity. I suppose this does answer why there aren't major flywheel installations are not present at nuclear powerplants.
One thought: why aren't there flywheel systems at wind turbines, moderated by a CVT? This would get rid of a lot of transformation losses, and since a motor is unneeded it would be fairly cheap.
There are two methods to throttle nuclear plants: by control rods, moderating neutron flux, and by temperature, moderating coolant flow (in, say, a pebble bed reactor). Either of these work well for generating heat, though coolant flow is simpler technically. Beyond this the plant is a steam turbine, which would have the same maintenance problems as any other steam turbine designed for the load. It's not as fast as gas, but the fuel is cheaper. But as DabAsteroid pointed out, Nuclear Plant are typically base loaded, in the US at least, so that's not terribly relevant.
I don't understand enough of the specifics of the particular designs Dab alludes to to comment on reactor poison buildup. I know that in pebble bed reactors throttling was intended by design.
I think that within the US market (which was, erroneously on my behalf, what I assumed the conversation was about), the point of new power plants not being yet created still holds: whatever load balancing one would need is an investment already made. (though this is mostly irrelevant to the point of discussion where nuclear plants don't supply peak demand). Of the proposals for which nuclear plants would supply peak power, the question is still out there: how will they balance the load? There are many possibilities, but they're mostly guesses. There is, increasingly, a diverse market for load balancing technology, and companies, struggling with technology and sales and tradition and economy, to try fill that need.
There are also resistive shunts that can be used in conjunction with an entire national 100%-nuclear fleet running at full throttle full-time. The resistive shunts would be used to simply dump any excess power. We use resistive shunts for this, today (which is how we get rid of wind and solar power that grid utilities are required to "buy" from the public), but in the proposed scenario, they would be used even more. To encourage demand during times of excess supply, a real-time free-market could help.
I envision that demand fluctuations would be smaller in the future, because of larger overall demand dwarfing weather/seasonal/earthspin-related (paganistic) heating and cooling fluctuations, and because of a global move toward a continuous day (after all, many of us are up in the "middle of the night", here, making our "day" when we feel like it).
Nuclear powerplants, typically, are capital intensive. For this reason, their operators aim for high capacity-factors. Unless economic forces are being ignored, they cannot easily be throttled. They run at 100%, all of the time, except when they are being refueled. The only nation that uses its nuclear powerplants in load-following mode is France -- since such a high proportion, some 80%, of its electricity is nuclear -- and France pays a price for that.
Additionally, it is not mechanically good for a nuclear-powerplant to throttle up and down. Such cycling causes parts to wear-out faster. If it is going to be used at all, it is best to keep it on, at a steady output.
There are other considerations. The nature of reactor poison build-up is such that throttling-up immediately after throttling-down tends, in typical reactor designs, to be difficult to do.
Unlike nuclear-powerplants, hydro and gas-turbine powerplants load-follow well (though the more-efficient gas-turbine powerplants take longer to start-up and might have to burn fuel, idling).
new [nuclear powerplants] aren't being created.The United States continuously adds nuclear capacity (through uprates, improved management, refurbishment of previously shut-down reactors, etc.). (http://www.eia.doe.gov/neic/press/images/press191_02-06-1.gi...)(http://uspowerpartners.org/images/Section2Topic-NuclearEnerg...) Additionally, up to 33 reactor-units are expected to be on-order there, soon. (http://www.world-nuclear.org/info/inf41.html#preparing) Several reactor-vessels have already been ordered for new reactor-units to be built in the United States. Worldwide, 36 power-reactor-units are under construction, 97 are planned, and 221 are proposed.
http://www.world-nuclear.org/info/reactors.html
Japan's nuclear share of its total electricity production (past and projected):
http://www.world-nuclear.org/info/inf79.html
It has 3 reactor-units under construction, and 12 more are planned.South Korea's nuclear share of its total electricity production (past and projected):
http://www.world-nuclear.org/info/inf81.html
It has 4 reactor-units under construction, and 4 more are planned.