Storage is a problem that simply needs to be solved for any green solution. Nuclear and wind included.
A big issue is that solar, wind, and nuclear simply don't play well together. Nuclear wants to be a base load, solar and wind push down the maximum base load feasible.
Without storage to smooth out the demand curve, you can't efficiently operate either.
I think the latter is more feasible without too much wind, since solar predictably goes to zero when demand is lowest. I don't think it's at all clear that a grid with high amounts of wind instead of nuclear would be cheaper.
Today, I agree that if we could make the switch overnight that solar + storage would probably be a lot more expensive than nuclear + storage.
However, who knows in 10 years. I could see liquid metal batteries becoming extremely economical.
The optimist in me believes that we'll eventually get good enough at solving the unit commitment problem in the energy grid that we'll reduce the need for carbon-intensive peaking sources and eventually even eliminate nuclear power. But we're not there today.