unless you're ok with a power grid that goes down regularly for unknown lengths of time, they [wind and solar] just can't hack it yet. To make sure that doesn't happen, you still have to build enough conventional power carry the full load.
The full load. Seems plausible, doesn't it? I thought the same, until I did a little research.
It turns out that there are large industrial users that can work around power availability, provided that they have reasonable notice and that averaged over a week the supply is ample. Quarries, for instance. Solar power is quite predictable, and in most places wind is fairly predictable up to a week in advance--very predictable, four to eight hours in advance nearly everywhere.
Electricity demand seems to be declining, and not only because of the hidden depression. The trend started about a decade back. Existing fossil plant will be plenty, until enough wears out.
Eventually existing plant will wear out, though. For winter supply in the north, and for summer afternoon peaks, increasing electricity price just a little would unleash the enormous potential electricity saving from better insulation and building airtightness with active counterflow heat-recovery ventilation.
Finally, nuclear, hydro, and biomass can supply base load--say 25% of annual peak. (Nuclear and hydro currently supply 12%; with declining demand, the proportion will rise if they are maintained at current levels.)There's plenty of room in the base load supply to charge all those electric cars. In some places pumped-storage hydro is viable; in others, compressed air energy storage is.
So, yes, some standby NG plant will be needed. Not for 100% of current capacity, though. To make sure the plant is built, we need a market in capacity to supply as well as the one in actual production.
TL;DR: With reasonably judicious, fair regulation and reasonably fair markets, including a market in capacity to supply, there's no problem. In thirty years, people could end up more comfortable and healthy at less cost than now, with a 97% reduction in fossil fuel use. Deary me.