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It's not a red herring in this sense. The big issue with solar power, especially in homes is what to do when the sun goes down. At certain times of the year, notably in winter, the peak power demands are in the early evening, just after sunset and in the morning, before the sun is high enough to provide much power from the PVs. If you don't have smart metering in your area, or you only get credit for returned electricity at the rate prevalent at the hour it goes back, you end up getting a credit for your returned electricity at a lower rate, or having to store it somehow, and in either event, you will end up buying electricity at the highest rate.
In many ways the interjection of "solar energy" is a red herring in
this news brief and in the article in "Science". As I understand
straight normal electrolysis, H and O are generated. These after
leaving the electrodes they may form H2 and O2, releasing a fair
fraction of the energy needed in the electrolysis. The group form MIT
have improved the efficiency of electrolysis by forming H2 and O2
directly at the electrode which does require less energy than forming H
and O. Additionally, the setup is simpler than the previous systems and
works with a less expensive, less picky and less toxic brew.