You're confused, negative prices are not driven by techincal limitations. Solar, and especially hydro, and even nuclear can shut down just fine.
Solar and Wind instead drive prices negative because they have subsidized contracts. Each country is slightly different in implementation, between Feed-in-Tarif vs Feed-in-Premium. In either method there will exist prices which are negative to the market but positive to the producer.
Thus if you cannot plan long term to rely on negative prices. Those FIT schemes around the world are transforming into FIP, and the FIP premiums are getting lower and lower. Negative pricing in electricity markets will go away in a decade or two. This isn't magic or even special, solar is succeeding which means the subsidies are getting weakened.
Curtailing solar production is not a big deal. How many existing plants have grid operator directed shutoffs depends on your market. In Japan as of 2024 all new non-rooftop solar has it. Prior to 2020ish only Kyushu and Kansai regions required it. Now Tepco, Hokkaido, and Touhoku require it for new contracts. There are still a couple old contracted plants getting developed this year, but those are rarities.
And that's only Japan, which itself does not have a super strong duck curve yet: http://jepx.org/ Regions like California have had extreme duck curves for ages. While duck curves are a big worry for internet commentors, they've been points of discussion for grid operators are a lot longer. Hence the move to Feed in Premiums which will slowly make the duck curve a solar operator's problem and not a tragedy of the commons situation.