I do think that nuclear is dead, because it takes government money to build it and because you don't win elections by subsidizing something that most people are scared of. Yes, nuclear is significantly more expensive than coal and slightly more expensive than gas and it takes 10-15 years to get a new nuclear plant online, which is longer than for any other power source. No sane capitalist would let any of his money anywhere near that investment unless the government promised to provide lots of subsidies.
With that said, the storage problem for solar and wind is absolutely not solved, nor will it be cheap. The amount of installed wind and solar is still so small that existing hydro dams can handle the storage, but wind and solar are growing fast enough that hydro dams will be completely insufficient.
There are experimental ideas about using excess power to make hydrogen, or methane or other hydrocarbons, but those are highly experimental and it is doubtful whether it will ever make economic sense. There are some very promising developments in turning sunlight directly into hydrogen or hydrocarbons, which will probably make a lot more sense economically. The problem is that none of this is available off the shelf, nor will it be in the next 5-10 years, and when it finally does become available it will take several decades to ramp up production to a level needed to supply 10+ billion people with energy storage.
Energy distribution has been making slow but steady progress over the last 150 or so years. We can easily transmit power 1000-2000 km today. Some day we'll be able to transmit it 3000 km and in the distant future 4000 km and 5000 km, which will be enough that we'll barely need storage. But again we're talking about decades into the future.
The nice ting about nuclear power is that we can build it now. You can call GE and order a plant on Monday, assuming you have the $5 billion (or $10 billion after the usual cost overrun) that they want for one of those and in 10-15 years you, your kids, grandkids and great-grandkids will have a clean and safe power plant. Throw in a few hundred millions for a decent sea wall if you decide put it next to the ocean.
If you are concerned about what future generations will do with your nuclear waste storage sites, you should probably be more concerned about what they will do (or rather what they will fail to do) with your hydro dams. I wouldn't trust a government that fails to repair bridges before they collaps to maintain a hydro dam upstream from where I live.