That's evening peaker gas plants in most places. After batteries push gas out of that market they go on to morning peaks and so on.
The UK for example basically doesn't have "peakers". Right now it's early evening, demand is high as people cook evening meals but haven't yet retired to bed where they stop using electricity, but renewable generation is reduced as the sun approaches the horizon. So there's 8GW of combined cycle gas power plant production, but only about 100MW of "peakers" and it might grow to 200MW or so at absolute peak.
This is being done at scale in California and Texas.
New advances in nuclear is what I hope for. First experimental SMRs are being installed in several places of the world, others are in design stage. Looks like a hopeful technology.
48 hours in Scandinavia is roughly equivalent to turning all their road vehicles electric. And that's even with Norway using the second highest per-capita rate of electricity in the world let alone Scandinavia (second to Iceland, whose electricity is 100% renewables thanks to abundant geothermal): https://www.statista.com/statistics/383633/worldwide-consump...
Given nobody is suggesting an instantaneous transition, this is not at all unrealistic, and I don't know why anyone might consider it to be.
Good luck with new nuclear, but with all the politics in that domain, I don't expect that to work out even if e.g. Helion Energy supplies working shipping-container-sized aneutronic fusion.
And everything you're talking about is an issue with any kind of production, I don't know why you're bringing it up as if it's unique to solar. If you're building a factory that needs high amounts of stable power then you plan accordingly. Doesn't change the fact that solar is a useful way to generate electricity. I don't think anyone is saying we have to use it exclusively. We can use different solutions for different problems.