If solar were free, but we still needed to pay for battery storage, how would it then compare in cost to fuel-based alternatives (fossil fuel, nuclear etc)?
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Maybe when we have smaller houses and don't have a bajillion devices plugged in all the time.
That could add maybe US$2000 per TEU, which is 21 tonnes of cargo such as solar panels. You can ship a TEU anywhere in the world for US$3000 or less. A 1m² solar panel might weigh 20 kg, so that's roughly 1000 solar pannels, or US$2 per solar panel. That solar panel is about 200 Wp, so this works out to US$0.01 of shipping cost per peak watt. Or less.
The solar module itself costs some US$0.18/Wp wholesale (the article cites higher prices, but see http://pvinsights.com/ https://www.solarserver.de/pv-modulpreise/ https://www.energytrend.com/solar-price.html for more detailed and reliable pricing info), and the whole installation including the panels maybe US$0.50/Wp. So there's no way that an extra US$0.01/Wp could double the cost of the installation. Bump it by 2% maybe.
China isn't the source of key materials. There aren't any key materials; the ingredients in PV cells, except for silver, are abundant everywhere. It's the source of the fully manufactured photovoltaic modules, a finished product that you can prop up in the sun and connect to a battery through a diode. If shipping costs were so high relative to the value of the finished product, every country would have its own solar-cell manufacturing plants, the way every country has its own liquid-oxygen plants, and there wouldn't be such a thing as a worldwide concentration of PV manufacturing in China.