They seem to be talking about each satellite managing the luminosity of the full moon over a few square kilometres, and getting a few tens of thousands of them.
Even if you ignoring how much drag these must have, and hence how much electrical power you'd need for an ion drive just to keep them up, each spot being a few km across (and only getting light while the satellite is over your horizon) is just not compelling.
Given most people don't have any reason to illuminate several square kilometres at once, for realistic scenarios it will take a lot of satellites before you beat the cheap battery-powered floodlights in my local Aldi or Kaufland, and the batteries in those lasts a lot longer than the 10-15 or so minutes each of the satellites will be over the horizon, and reflectors like these can only supply sunlight close to sunset otherwise the earth blocks the sun from them.
In the list of things which, if you could make them at all useful, would also be relatively easy to redesign as weapons.
This has pretty obvious military applications in addition to the "solar all day" application.
With global warming, trillions upon trillions of acres of immensely fertile bogland, in Northern Canada is thawing. The problem is, global warming doesn't affect daylight. 4 hours of "the sun barely makes it over the horizon" means no crops, no matter if the temp is above 0C in September.
Obviously this satellite isn't viable, but all things start small. Large tracts of land could be illuminated.
But of course, I question the logic of redirecting more sunlight, especially such large amounts, onto a world already warming uncontrollably.
Still, it could be useful for the polar caps on Mars?
These seem like unlikely things though.
In regards to people with reasons to illuminate several sq km at once - I'd bet that major metro areas would see a massive savings in electricity/maintenance if these were deployed over a metro region. Whether that is more than the cost of a satellite? Who knows, it's still fiction until these people try it out. But it's at least an interesting use case.
> relatively easy to redesign as weapons
There is a fiction I've read years ago that mentioned satellites becoming makeshift weapons by overheating exposed objects (think reactors, gas trucks, oil refineries) by acting as a solar furnace [1] via mirrors.
Not sure/don't recall how it deals with practical issues such as clouds and distance/intensity, but good enough for a story I guess.
[1]: https://en.wikipedia.org/wiki/Solar_furnace