Nuclear reactors cannot modulate their level of output several times per day...
That's true of solid fuel reactors. Liquid fuel reactors like LFTR can have their output follow the load.
I'm a big fan of hydro power, it's cheap, clean, and safe. The problem with hydro is that we've pretty much run out of rivers to dam. I'm sure that there are more places we could put in hydro but they are few. One example, there was a small hydro dam not far from where I grew up that was severely damaged in a flood. There's currently no plans to repair it since it's just not profitable any more.
Right now hydro is the only viable technology we have for grid level electric storage. I suspect that hydro will play a big role in load leveling for solid fuel nuclear, wind, and solar. If the tree huggers won't let us take advantage of our vast supplies of coal, natural gas, and oil then we will need to develop liquid fuel nuclear power. Otherwise we're going to exceed the load following capability of our hydro sources real quick.
The problem with liquid fuel nuclear lies primarily with the laws. Until we fix the laws we are stuck with fossil fuels. We've dammed up all the rivers that we can and the only other technology we have for load following is natural gas turbines. If we fix the laws so we can have LFTR then we won't be arguing about the carbon footprint of electric cars anymore. I do suspect we would still be arguing about the crappy range and recharge times though. I think the physics will always be against us on that one, it's real hard for electricity to compete with the wattage that comes from a gasoline pump.