Most of the time you can get away with a relatively small amount of storage but sometimes you get an extended "dry spell", so you might need two weeks or more storage to be entirely reliable.
Renewables have been workable so far because of low-cost gas turbines fired by methane that take up the slack: we know now that methane is 80 or so times more potent a global warming gas than carbon dioxide, so if you lose 1% of the gas in handling it is a big problem.
The fact is that nuclear waste is not waste. The light water reactor extracts about 1% of the energy that a fast reactor could extract from uranium. In fact, molten salt fast reactors can not only consume plutonium and other actinides but also destroy a good fraction of the most dangerous fission products.