Yes, solar can help meet peak load during the summer, but not the rest of the year and it causes stress on the system by requiring a lot of power to spin up to meet demand and solar decreases.
You don't know when peak demand in California was yesterday, because you're looking at a graph of the utility company's electricity production, not electricity demand. You'd need to add all the self-consumption by "behind-the-meter" solar installations on homes and businesses to find out the real demand peak. From the perspective of CAISO, solar self-generation is indistiguishable from reduced demand.
We know from historical figures that the absolute highest yearly peak in California, the one that you need to build your grid to withstand at great expense even if it only requires that load for a short period of time per year correlates well with solar, and so solar saves lots of money by shaving that peak.
The "duck curve" is also not a demand curve, it's demand, minus self-generated-solar, minus grid-generated-solar. And even then, it only appears in the winter months, when demand in California is on the low end of the yearly cycle something like a third of peak demand in the summer months. (Note the graphs showing the duck curve in your second link are from January and March).
I don't think that explains everything about the demand curve, but using the current day demand curve to say 'solar doesn't work' isn't looking deeply enough.
I like the Arthur Clarke quote: When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong. - Arthur C. Clarke
Note that Solar isn't "hurting". Because such demand right now is being covered by Natural Gas Peaker Plants anyway.
Natural Gas Peaker plants are expensive, so if we can replace some of their usage with other energy sources, that'd be great. Eventually, we might be able to transition off of them with sufficiently advanced energy storage technologies.
And once baseload power starts getting "replaced", we enter the realm of coal plants and nuclear plants reconditioning themselves so that they can be scaled up and down a bit better.
I know both coal and nuclear power require many minutes to change their energy production, but if a smaller-scale energy storage (~30 minutes) can be created to hold out during the scaling up / down period, the problem could be solved.
As opposed to say, load-shifting pure solar energy (which requires a storage capacity measured in hours, not minutes). High power / low time can be solved with standard Lead Acid batteries or maybe Flywheels (cheaper technology than Lithium Ion, which would be better for hours of storage)
https://www.raponline.org/featured-work/teach-the-duck-to-fl...
Industries and homes find innovative ways to adapt to market pricing. All the appliances there have options to use power at night (when it is cheaper there). For solar, the times may be different but the same idea remains. Commercial power is priced at a premium when the grid is overloaded (typically winter months).
[1] http://residential.edf.com/energy-at-home/offers/electricity...
That's a very specific claim, and I don't think your cited graph even supports it.
Presumably, you say "this time of year" because you know that the yearly peak in California is driven by air-con usage in the summer afternoons, which correlates very well with solar.
But even right now, in early May, the graph is mostly flat through the afternoon and evening, with only the slight peak at 8 or 9 at night making your statement true in a very narrow sense.
Notably however, the graph only includes grid side solar production, so panels on homes or business roofs are not included in the graph. If you added those to the total demand curve would shift upwards during solar production hours.