Remember, we're talking about a world where building renewables to 4x peak demand would be actually economical.
This works on the same principle as an insurance market: it's likely that even at 4x capacity, your local solar farm has a few cloudy days. It's highly unlikely that your entire regional grid generation falls below demand. That probability falls (super?-)exponentially in the size of the region.
Taking a step back: yes, renewable power is intermittent and you need electricity here, now. Either 1) transmit from elsewhere, 2) store locally, or 3) supplement with a stable source (nuclear / thermal). The choice simply comes down to cost (to provide a given level of reliability).
The most efficient solution is likely to do all of the above, taking local conditions into account. Adjusting for local conditions is one thing that a (well-managed) market helps tackle.